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Relevant bibliographies by topics / Zero exponents

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Academic literature on the topic 'Zero exponents'

Author: Grafiati

Published: 4 June 2025

Last updated: 6 July 2025

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Journal articles on the topic "Zero exponents"

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GELFERT, KATRIN, and MICHAŁ RAMS. "The Lyapunov spectrum of some parabolic systems." Ergodic Theory and Dynamical Systems 29, no. 3 (2009): 919–40. http://dx.doi.org/10.1017/s0143385708080462.

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AbstractWe study the Hausdorff dimension for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given lower and upper Lyapunov exponents and, in particular, with zero lower Lyapunov exponent. We prove that the level set of points with zero exponent has full Hausdorff dimension, but carries no topological entropy.

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SAMOSHCHENKO, O. V. ""EXPONENT CALCULATION OF FLOATING-POINT NUMBERS WITH SHIFTED ENCODING A POZITIVE ZERO"." Scientific papers of Donetsk National Technical University. Series: Informatics, Cybernetics and Computer Science 1, no. 40 (2025): 105–10. https://doi.org/10.31474/1996-1588-2025-1-40-105-110.

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"The rule for calculating the exponent of floating-point numbers in the shifted encoding system with positive zero is indicated, which provides for the original representation of exponents in a combination of a complementary code and a code with positive zero. Mathematical expressions are formulated to fix the overflow of the exponent of the normalized and denormalized mantissa product, according to which an arithmetic device is synthesized. It is shown that in the absence of overflow, the correct code of the exponent of the mantissa product with a violation of normalization is formed by adding a polynomial of a unit constant. The correctness of the sum of exponents at the output of the adder is determined by the output carry and the sign bit of the exponent of the product. Overflow of the bit grid of the mantissa product with a violation of normalization is determined by the combination of the signs of overflow of the normalized code and the zero value of the code at the main outputs of the exponent adder. The range of change of the total sum at the adder outputs when calculating exponents in the system of shifted codes with positive zero is analytically determined. Logical expressions are synthesized for fixing the polarity of overflow in the arithmetic device. The correctness of using the code of converted operands when calculating binary values of exponents is confirmed in examples."

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BARAVIERA, ALEXANDRE T., and CHRISTIAN BONATTI. "Removing zero Lyapunov exponents." Ergodic Theory and Dynamical Systems 23, no. 6 (2003): 1655–70. http://dx.doi.org/10.1017/s0143385702001773.

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Sekikawa, Munehisa, and Naohiko Inaba. "Chaos after Accumulation of Torus Doublings." International Journal of Bifurcation and Chaos 31, no. 01 (2021): 2150009. http://dx.doi.org/10.1142/s0218127421500097.

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A recent paper investigates the bifurcation diagrams involved with torus doubling and asserts that the chaotic attractors observed after torus doubling have two Lyapunov exponents that are exactly zero. Against this assertion, we claim that the absolute value of one of the calculated zero Lyapunov exponents is not exactly zero but is instead slightly positive, because successive torus doubling is constrained by a very small underlying parameter. We justify our position by calculating Lyapunov spectra precisely using an autonomous piecewise-linear dynamical circuit. Our numerical results show that one of the Lyapunov exponents is close to, but not exactly, zero. In addition, we consider coupled logistic and sine-circle maps whose dynamics express the fundamental mechanism that causes torus doubling, and we confirm that torus doubling occurs fewer times when the coupling parameter of this discrete dynamical system is relatively larger. Consequently, the absolute value of the second Lyapunov exponent of this discrete system does not approach zero after the accumulation of torus doubling when the coupling parameter is set to larger values.

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Hikmahturrahman, Hikmahturrahman, Suhardiman Darson Tamu, Nosva Adam Yunus, Febiyanti R. Hasan, and Rizal Masaniku. "Mathematics Education Students' Understanding of Exponent Concepts Based on Cognitive Style." Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi 13, no. 1 (2025): 9–13. https://doi.org/10.37905/euler.v13i1.30137.

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This study aims to explore the understanding of the concept of exponents of mathematics education students in terms of cognitive style. This type of research is qualitative with a case study approach. The subjects in this study were 2 mathematics education students consisting of 1 student with reflective cognitive style and 1 student with impulsive cognitive style. The instruments used in this study were 2 items of exponent problem solving and interview guidelines. The results showed that Reflective Cognitive Style Subjects were able to fulfill all indicators of understanding the concept of exponents, namely indicators of exponent problem solving, identifying positive, negative, and zero exponents, using exponent rules, understanding roots and fractions as exponents, and identifying and correcting exponent misconceptions. Meanwhile, Impulsive Cognitive Style Subjects were only able to fulfill 4 indicators of understanding the concept of exponents. Impulsive Cognitive Style Subjects were not able to fulfill the indicators of identifying and correcting exponent misconceptions. The advantage in this study is to fill the gap in the literature by connecting the understanding of the concept of exponents and cognitive style variations. Furthermore, making mathematics education students as research targets. It offers novelty because their understanding of exponents has direct implications on how they teach the concept in the future.

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Alexakis, A., and F. Pétrélis. "Critical Exponents in Zero Dimensions." Journal of Statistical Physics 149, no. 4 (2012): 738–53. http://dx.doi.org/10.1007/s10955-012-0615-6.

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Carpintero, D. D., and J. C. Muzzio. "The Lyapunov exponents and the neighbourhood of periodic orbits." Monthly Notices of the Royal Astronomical Society 495, no. 2 (2020): 1608–12. http://dx.doi.org/10.1093/mnras/staa1227.

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ABSTRACT We show that the Lyapunov exponents of a periodic orbit can be easily obtained from the eigenvalues of the monodromy matrix. It turns out that the Lyapunov exponents of simply stable periodic orbits are all zero, simply unstable periodic orbits have only one positive Lyapunov exponent, doubly unstable periodic orbits have two different positive Lyapunov exponents, and the two positive Lyapunov exponents of complex unstable periodic orbits are equal. We present a numerical example for periodic orbits in a realistic galactic potential. Moreover, the centre manifold theorem allowed us to show that stable, simply unstable, and doubly unstable periodic orbits are the mothers of families of, respectively, regular, partially, and fully chaotic orbits in their neighbourhood.

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FERREIRA, A. L., and E. L. PRODANESCU. "FISHER SCALING IN TWO-DIMENSIONAL ISING MAGNETIC LATTICE-GAS." International Journal of Modern Physics C 16, no. 01 (2005): 45–60. http://dx.doi.org/10.1142/s0129183105006929.

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The critical properties of two-dimensional Ising magnetic lattice-gas model are studied by Monte-Carlo simulation in the canonical ensemble. The results are analyzed considering the modified Fisher scaling for systems with zero specific heat exponent, which applies when there are constrained variables such as the density in the canonical ensemble. The estimates of the exponents are obtained and compared to the exponents of the Ising universality class to which the model is expected to belong.

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Loboda, Nadezhda A. "Comparing the spectra of wandering exponents of a nonlinear two-dimensional system and a first approximation system." Russian Universities Reports. Mathematics, no. 146 (2024): 176–87. http://dx.doi.org/10.20310/2686-9667-2024-29-146-176-187.

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In this paper, we study various varieties of wandering exponents for solutions of linear homogeneous and nonlinear two-dimensional differential systems with coefficients continuous on the positive semiaxis. Moreover, all non-extendable solutions of the nonlinear system under consideration are defined on the entire positive time semi-axis. In 2010, I.N. Sergeev determined the wandering speed and wandering exponents (upper and lower, strong and weak) of a nonzero solution x of a linear system. The wandering speed of the solution is the time-average velocity at which the central projection of the solution moves onto the unit sphere. Strong and weak exponents of wandering are the wandering speed of the solution, but minimized over all coordinate systems, and in the case of a weak exponent of wandering, minimization is performed at each moment of time. Therefore, strong and weak exponents of wandering take into account only the information about the solution that is not is suppressed by linear transformations: for example, they take into account the revolutions of the vector x around zero, but do not take into account its local rotation around some other vector. In this work, a first approximation study of strong and weak wandering exponents was carried out. It is established that there is no dependence between the spectra (i.e., a set of different values on non-zero solutions) of strong and weak wandering exponents of a nonlinear system and the system of its first approximation. Namely, a two-dimensional nonlinear system is constructed such that the spectra of wandering exponents of its restriction to any open neighborhood of zero on the phase plane consist of all rational numbers in the interval [0,1], and the spectra of the linear system of its first approximation consist of only one element.

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ARNAUD, M. C. "Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting." Ergodic Theory and Dynamical Systems 33, no. 3 (2012): 693–712. http://dx.doi.org/10.1017/s0143385712000065.

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AbstractWe consider locally minimizing measures for conservative twist maps of the $d$-dimensional annulus and for Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. For weakly hyperbolic measures of such type (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and unstable Oseledets bundles gives an upper bound on the sum of the positive Lyapunov exponents and a lower bound on the smallest positive Lyapunov exponent. We also prove some more precise results.

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Dissertations / Theses on the topic "Zero exponents"

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Medvedyeva, Kateryna. "Characteristic properties of two-dimensional superconductors close to the phase transition in zero magnetic field." Doctoral thesis, Umeå : Univ, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-102.

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Lee, Feng-Tien, and 李豐田. "Critical Exponents and Zeros of the Partition Function of Ising Model for a Class of Hierarchical Lattices." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/28207517283262726549.

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博士<br>中原大學<br>物理學系<br>87<br>We shall study the critical behavior of the Ising model on hierarchical lattices. We first obtain the renormalization maps for various hierarchical lattices. Based on the renormalization maps we obtain critical exponents, reduced free energy per bond, and zeros of partition functions. Then we analyze the effects of the geometric structure of an MKH (Migdal-Kadanoff Hierarchy) on the Ising model. The geometric structure of an MKH is described by two factors in a basic cell: one is the number of strings, M, and the other is the number of vertices, A, in a string. We first study the variation of the critical behaviors, including the location of the critical temperature and the critical exponents, in terms of these two geometric factors, and then we study the distribution of complex zeros closest to the real temperature axis and observe their finite-size scaling behavior for various MKHs. Finally, we analyze the geometric effect on the global scaling properties of the Julia sets of the Fisher zeros of the partition function by studying the variations of generalized fractal dimensions and the singularity spectrum. We want to assess what degree of metric universality is there. There are two tools performed to analyze the metric properties of the Julia set. The first one is the famous thermodynamic formalism of multifractal analysis. The analysis is done on the basis of knowledge of the recursion relation of the multifractal invariant measure by calculating the generalized fractal dimensions and the singularity spectrum. The second one is the wavelet transform which has recently been developed. The basic idea is to calculate the Hölder exponent h of the measure and its D(h) singularity spectrum that the Hausdorff dimension of the set where the Hölder exponent is equal to h. From the analysis of our results, we find that the scaling law holds for hierarchical lattices as for regular lattices, but the universality concept is violated. The claim that the fractal dimension and the connectivity serve as criteria for universality of critical exponents on hierarchical lattices is not enough. It therefore seems that one has to introduce more parameters to distinguish completely these MKHs. On the other hand, it is found that there is no metric universality, although there are some aspects of metric universality shown in the multifractal behavior of Fisher zeros.

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Books on the topic "Zero exponents"

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Morrison, Phylis, and Philip Morrison. Powers of Ten (Scientific American Library Paperback). W.H. Freeman & Company, 1994.

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Book chapters on the topic "Zero exponents"

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Dias, João Lopes, and Filipe Santos. "Hyperbolicity or Zero Lyapunov Exponents for $$C^2$$-Hamiltonians." In New Trends in Lyapunov Exponents. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-41316-2_4.

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Hotanen, Toni. "Everywhere Zero Pointwise Lyapunov Exponents for Sensitive Cellular Automata." In Cellular Automata and Discrete Complex Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61588-8_6.

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Mueller, Carl, and Etienne Pardoux. "The Critical Exponent for a Stochastic PDE to Hit Zero." In Stochastic Analysis, Control, Optimization and Applications. Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1784-8_19.

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Bellare, Mihir, and Adriana Palacio. "The Knowledge-of-Exponent Assumptions and 3-Round Zero-Knowledge Protocols." In Advances in Cryptology – CRYPTO 2004. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-28628-8_17.

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Zhang, Tingting, Hongda Li, and Guifang Huang. "Constant-Round Leakage-Resilient Zero-Knowledge Argument for NP from the Knowledge-of-Exponent Assumption." In Information Security and Privacy. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19962-7_15.

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Grossmann, Atina. "No Zero Hour." In Reforming Sex. Oxford University PressNew York, NY, 1995. http://dx.doi.org/10.1093/oso/9780195056723.003.0008.

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Abstract This book ends with a discussion curiously similar to the one with which it began: German efforts to cope with defeat and postwar reconstruction and its perceived effects on women, family, and social health. Once again, the politics of reproduction and sexuality, and especially questions around abortion, birth control, and marriage and sex counseling, took center stage as a new welfare state (in this case, two new welfare states) was organized. But after 12 years of National Socialism, the repression of sex reform in the Soviet Union, and the exile of many of the most committed exponents of sex reform, the terms of debate had shifted.

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Vaidyanathan, Sundarapandian, Ahmad Taher Azar, Aceng Sambas, Shikha Singh, Kammogne Soup Tewa Alain, and Fernando E. Serrano. "A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation." In Advances in System Dynamics and Control. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-4077-9.ch013.

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This chapter announces a new four-dimensional hyperchaotic system having two positive Lyapunov exponents, a zero Lyapunov exponent, and a negative Lyapunov exponent. Since the sum of the Lyapunov exponents of the new hyperchaotic system is shown to be negative, it is a dissipative system. The phase portraits of the new hyperchaotic system are displayed with both two-dimensional and three-dimensional phase portraits. Next, the qualitative properties of the new hyperchaotic system are dealt with in detail. It is shown that the new hyperchaotic system has three unstable equilibrium points. Explicitly, it is shown that the equilibrium at the origin is a saddle-point, while the other two equilibrium points are saddle-focus equilibrium points. Thus, it is shown that all three equilibrium points of the new hyperchaotic system are unstable. Numerical simulations with MATLAB have been shown to validate and demonstrate all the new results derived in this chapter. Finally, a circuit design of the new hyperchaotic system is implemented in MultiSim to validate the theoretical model.

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"On the Dynamics of Some Nonhyperbolic Area-preserving Piecewise Linear Maps." In Mathematics in Signal Processing V, edited by Peter Ashwin and Xin-Chu Fu. Oxford University PressOxford, 2002. http://dx.doi.org/10.1093/oso/9780198507345.003.0012.

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Abstract There are several situations in signal processing where systems are well-modelled by area-preserving discontinuous systems that are either exactly or close to being piecewise linear. In particular, the overflow oscillation problem for lossless digital filters [1]. and band pass sigma-delta modulator dynamics [10] are examples of maps that display nontrivial dynamics, where the usual techniques of smooth hyperbolic nonlinear dynamics do not work. For example, all Lyapunov exponents may be zero.

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"Second Solution When the Exponents Differ by an Integer or Zero." In Asymptotics and Special Functions. A K Peters/CRC Press, 1997. http://dx.doi.org/10.1201/9781439864548-57.

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Farkhodjon Makhmadshoevich, Talbakov. "Approximation of Uniform Almost Periodic Functions by Inclusions and Integrals." In Beyond Signals - Exploring Revolutionary Fourier Transform Applications. IntechOpen, 2025. https://doi.org/10.5772/intechopen.1008170.

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The paper examines some issues of approximation of almost periodic Bohr functions from partial sums of the Fourier series and Marcinkiewicz means, when the Fourier exponents (function spectrum) of the functions under consideration have a limit point at infinity. The question of the deviation of a given function fx from its partial sums of the Fourier series is investigated, depending on the rate at which the value of the best approximation by a trigonometric polynomial of limited degree tends to zero. Here, when determining the Fourier coefficients, instead of the function under consideration, some arbitrary, real, continuous function is taken Φσtσ>0, which in a given interval is equal to one, and in other cases is equal to zero. Next, an upper estimate for the deviation of an almost periodic function in the sense of Bohr by Marcinkevich means is established in a similar manner.

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Conference papers on the topic "Zero exponents"

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Furon, Teddy. "About zero bitwatermarking error exponents." In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. http://dx.doi.org/10.1109/icassp.2017.7952533.

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Lou, Jingjun, and Shijian Zhu. "Three Conditions Lyapunov Exponents Should Satisfy." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48496.

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In contrast to the unilateral claim in some papers that a positive Lyapunov exponent means chaos, it was claimed in this paper that this is just one of the three conditions that Lyapunov exponent should satisfy in a dissipative dynamical system when the chaotic motion appears. The other two conditions, any continuous dynamical system without a fixed point has at least one zero exponent, and any dissipative dynamical system has at least one negative exponent and the sum of all of the 1-dimensional Lyapunov exponents id negative, are also discussed. In order to verify the conclusion, a MATLAB scheme was developed for the computation of the 1-dimensional and 3-dimensional Lyapunov exponents of the Duffing system with square and cubic nonlinearity.

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Banu, Eliza A., Dan Marghitu, and P. K. Raju. "Dynamics of Human Spine in Jumps Using Lyapunov Exponents." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12415.

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Characterizing and quantifying the local dynamics of the human spine during various athletic exercises is important for therapeutic and physiotherapy reasons or athletic related effects on the human spine. In this study we computed the largest finite-time Lyapunov exponents for the spine of a human subject during an athletic exercise for several volunteers. The kinematic data was collected using the 3D motion capture system (Motion Realty Inc.). Four healthy male subjects were asked to perform two sets of 30 jumps. In order to draw a conclusion about the chaotic nature of the dynamics of the lumbar spine Lyapunov exponent spectrum was calculated for each volunteer which included four Lyapunov exponents, one negative, one very close to zero and two positive. Subjects 1, 2 and 4 registered a significant increase in the largest Lyapunov exponent from the first set jumps to the next. Subject 3 registered no change in the values of Lyapunov exponents. Nonlinear analysis of the human spine demonstrates the chaotic nature of the system. The computation of the largest Lyapunov exponents enables a more precise characterization of the dynamics of the human spine.

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Palacio-Baus, Kenneth, and Natasha Devroye. "Two-Way AWGN Channel Error Exponents at Zero Rate." In 2018 IEEE International Symposium on Information Theory (ISIT). IEEE, 2018. http://dx.doi.org/10.1109/isit.2018.8437797.

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Korneyeva, Tatyana. "Zero Exponents in the Russian Language and Peculiarities of Their Learning." In IFTE 2020 - VI International Forum on Teacher Education. Pensoft Publishers, 2020. http://dx.doi.org/10.3897/ap.2.e1193.

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Marghitu, Dan B., and Prasad Nalluri. "Stability Analysis of Healthy Greyhounds via Lyapunov Exponents." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-0428.

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Abstract This paper evaluated the applicability of a mathematical technique of computing Lyapunov exponents for nonlinear systems to describe and define normal greyhound gait. A commercially available video based, 2-dimensional motion analysis system was utilized to acquire kinematic data from healthy greyhounds being led at trot. The removal of noise from the time series data obtained from measurements was accomplished with B-spline wavelets. Lyapunov exponents of five normal subjects were computed from the kinematic data. For the steady state animal locomotion one of the Lyapunov exponents was always zero and all other exponents were negative. Lyapunov exponents provided a useful characterization of the given experimental data set.

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SHUB, MICHAEL. "Non-zero random Lyapunov exponents versus mean deterministic exponents for a twist like family of diffeomorphisms of the two sphere." In XIVth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812704016_0019.

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Samoshchenko, Oleksandr, Irina Zeleneva, Heorhii Marhiiev, and Oleksandr Miroshkin. "Biased Exponents Encoding With Positive Zero When Comparing Absolute Values of Floating-Point Numbers." In 2020 IEEE International Conference on Problems of Infocommunications. Science and Technology (PIC S&T). IEEE, 2020. http://dx.doi.org/10.1109/picst51311.2020.9468077.

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Jedrzejewski, F. "Entropy and Lyapunov Exponents Relationships in Stochastic Dynamical Systems." In ASME 2003 Pressure Vessels and Piping Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/pvp2003-1822.

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Stochastic differential equations and classical techniques related to the Fokker-Planck equation are standard bases for the analysis of nonlinear systems perturbed by noise, such as seismic wave propagation in random media and response of structures to turbulent wind. In this paper, a complementary approach based on entropy production is proposed to analyse the stochastic stability of dynamical systems. For a large class of stochastic dynamical systems, it is shown that the entropy information production is equal to the negative sum of Lyapunov exponents as the noise strength tends to zero. This result is correlated to the topological entropy property, which is in some cases such as the hyperbolic case, equal the sum of Lyapunov exponents. Several examples are given to illustrate the proposed procedure.

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Palacio-Baus, Kenneth, and Natasha Devroye. "Variable-length Coding Error Exponents for the AWGN Channel with Noisy Feedback at Zero-Rate." In 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019. http://dx.doi.org/10.1109/isit.2019.8849578.

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