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Journal articles on the topic 'Algebraic dynamics'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

VIALLET, C. M. "ALGEBRAIC DYNAMICS AND ALGEBRAIC ENTROPY." International Journal of Geometric Methods in Modern Physics 05, no. 08 (2008): 1373–91. http://dx.doi.org/10.1142/s0219887808003375.

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We give the definition of algebraic entropy, which is a global index of complexity for dynamical systems with a rational evolution. We explain its geometrical meaning, and different methods, heuristic or exact to calculate this entropy. This quantity is a very good integrability detector. It also has remarkable properties, which make it an interesting object of study by itself. It is in particular conjectured to be the logarithm of algebraic integer, with a limited range of values, still to be explored.

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2

Lindahl, Karl-Olof. "Applied algebraic dynamics." P-Adic Numbers, Ultrametric Analysis, and Applications 2, no. 4 (2010): 360–62. http://dx.doi.org/10.1134/s2070046610040084.

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3

Zhang, Hua, WeiTao Lu, and ShunJin Wang. "Algebraic dynamics solution and algebraic dynamics algorithm of Burgers equations." Science in China Series G: Physics, Mechanics and Astronomy 51, no. 11 (2008): 1647–52. http://dx.doi.org/10.1007/s11433-008-0156-9.

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4

Zhang, Shou-Wu. "Distributions in algebraic dynamics." Surveys in Differential Geometry 10, no. 1 (2005): 381–430. http://dx.doi.org/10.4310/sdg.2005.v10.n1.a9.

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5

Wang, ShunJin, and Hua Zhang. "Symplectic algebraic dynamics algorithm." Science in China Series G: Physics, Mechanics and Astronomy 50, no. 2 (2007): 133–43. http://dx.doi.org/10.1007/s11433-007-0013-2.

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6

Wang, Shunjin, and Hua Zhang. "Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations." Science in China Series G: Physics, Mechanics and Astronomy 49, no. 6 (2006): 716–28. http://dx.doi.org/10.1007/s11433-006-2017-8.

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7

Zhang, Hua, WeiTao Lu, and ShunJin Wang. "Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation." Science in China Series G: Physics, Mechanics and Astronomy 51, no. 10 (2008): 1470–78. http://dx.doi.org/10.1007/s11433-008-0148-9.

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8

MATSUNO, YOSHIMASA. "DYNAMICS OF INTERACTING ALGEBRAIC SOLITONS." International Journal of Modern Physics B 09, no. 17 (1995): 1985–2081. http://dx.doi.org/10.1142/s0217979295000811.

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A survey is made which highlights recent topics on the dynamics of algebraic solitons, which are exact solutions to a certain class of nonlinear integrodifferential evolution equations. The model equations that we consider here are the Benjamin-Ono (BO) and its higher-order equations together with the BO-Burgers equation, a model equation for deep-water waves, the sine-Hilbert (sH) equation and a damped sH equation. While these equations have their origin either in physics or in mathematics, each equation exhibits a novel type of algebraic soliton solution and hence its characteristic is worth

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9

Alonso, L. Martinez, and E. Olmedilla Moreno. "Algebraic geometry and soliton dynamics." Chaos, Solitons & Fractals 5, no. 12 (1995): 2213–27. http://dx.doi.org/10.1016/0960-0779(94)e0096-8.

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10

Leschber, Yorck, and J. P. Draayer. "Algebraic realization of rotational dynamics." Physics Letters B 190, no. 1-2 (1987): 1–6. http://dx.doi.org/10.1016/0370-2693(87)90829-x.

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11

Gogoussis, A., and M. Donath. "A Method for the Real Time Solution of the Forward Dynamics Problem for Robots Incorporating Friction." Journal of Dynamic Systems, Measurement, and Control 112, no. 4 (1990): 630–39. http://dx.doi.org/10.1115/1.2896188.

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A modular and computationally efficient method for solving the forward dynamics problem of robot mechanisms incorporating Coulomb friction is developed. This hybrid approach incorporates both analog and digital components that facilitate real time solutions. Coulomb friction effects associated with both transmissions and bearings are considered. Moreover, the methods accounts for joint flexibility as well as actuator gyroscopic effects. In our approach, the inverse dynamics formulation is used for solving the forward dynamics problem. The positive definiteness property of the inertia matrix of

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12

ADAMCZEWSKI, BORIS, та YANN BUGEAUD. "Dynamics forβ-shifts and Diophantine approximation". Ergodic Theory and Dynamical Systems 27, № 6 (2007): 1695–711. http://dx.doi.org/10.1017/s0143385707000223.

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AbstractWe investigate theβ-expansion of an algebraic number in an algebraic baseβ. Using tools from Diophantine approximation, we prove several results that may suggest a strong difference between the asymptotic behaviour of eventually periodic expansions and that of non-eventually periodic expansions.

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13

Srivastava, Sunita, C. N. Kumar, and K. Tankeshwar. "Dynamics of gelling liquids: algebraic relaxation." Journal of Physics: Condensed Matter 21, no. 33 (2009): 335106. http://dx.doi.org/10.1088/0953-8984/21/33/335106.

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14

Wang, ShunJin, and Hua Zhang. "Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems." Science in China Series G: Physics, Mechanics and Astronomy 51, no. 6 (2008): 577–90. http://dx.doi.org/10.1007/s11433-008-0055-0.

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15

Robinson, James D., and M. John D. Hayes. "THE DYNAMICS OF A SINGLE ALGEBRAIC SCREW PAIR." Transactions of the Canadian Society for Mechanical Engineering 35, no. 4 (2011): 491–503. http://dx.doi.org/10.1139/tcsme-2011-0029.

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The algebraic screw pair, or A-pair, represents a new class of kinematic constraint that exploits the self-motions inherent to a specific configuration of Griffis-Duffy platform. Using the A-pair as a joint in a hybrid parallel-serial kinematic chain results in a sinusoidal coupling of rotation and translation between adjacent links. The resulting linkage is termed an A-chain. This paper reveals the dynamic equations of motion of a single A-pair and examines the impact of the inertial properties of the legs of the A-pair on the dynamics. A numerical example illustrates the impact of the leg ef

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16

Xie, Junyi. "Algebraic dynamics of the lifts of Frobenius." Algebra & Number Theory 12, no. 7 (2018): 1715–48. http://dx.doi.org/10.2140/ant.2018.12.1715.

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17

Majidi-Zolbanin, M., N. Miasnikov, and L. Szpiro. "Entropy and flatness in local algebraic dynamics." Publicacions Matemàtiques 57 (July 1, 2013): 509–44. http://dx.doi.org/10.5565/publmat_57213_12.

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18

Bagarello, F., and C. Trapani. "Algebraic dynamics inO*-algebras: A perturbative approach." Journal of Mathematical Physics 43, no. 6 (2002): 3280–92. http://dx.doi.org/10.1063/1.1467609.

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19

LI, ZHIQIANG, and DAIZHAN CHENG. "ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS." International Journal of Bifurcation and Chaos 20, no. 03 (2010): 561–82. http://dx.doi.org/10.1142/s0218127410025892.

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Using semi-tensor product of matrices, a matrix expression for multivalued logic is proposed, where a logical variable is expressed as a vector, and a logical function is expressed as a multilinear mapping. Under this framework, the dynamics of a multivalued logical network is converted into a standard discrete-time linear system. Analyzing the network transition matrix, easily computable formulas are obtained to show (a) the number of equilibriums; (b) the numbers of cycles of different lengths; (c) transient period, the minimum time for all points to enter the set of attractors, respectively

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20

Toutounji, Mohamad. "Algebraic approach to electronic spectroscopy and dynamics." Journal of Chemical Physics 128, no. 16 (2008): 164103. http://dx.doi.org/10.1063/1.2903748.

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21

Valls, Claudia. "Invariant algebraic surfaces for a virus dynamics." Zeitschrift für angewandte Mathematik und Physik 66, no. 4 (2014): 1315–28. http://dx.doi.org/10.1007/s00033-014-0464-z.

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22

Pineiro, Jorge. "Heights, algebraic dynamics and Berkovich analytic spaces." São Paulo Journal of Mathematical Sciences 3, no. 1 (2009): 77. http://dx.doi.org/10.11606/issn.2316-9028.v3i1p77-94.

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23

Panakkal, Susan Mathew, Parameswaran R, and M. J. Vedan. "A geometric algebraic approach to fluid dynamics." Physics of Fluids 32, no. 8 (2020): 087111. http://dx.doi.org/10.1063/5.0017344.

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24

Ghioca, Dragos, and Junyi Xie. "Algebraic dynamics of skew-linear self-maps." Proceedings of the American Mathematical Society 146, no. 10 (2018): 4369–87. http://dx.doi.org/10.1090/proc/14104.

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25

Wang, D. "Algebraic analysis of stability and bifurcation for nonlinear flight dynamics." Aeronautical Journal 115, no. 1168 (2011): 345–49. http://dx.doi.org/10.1017/s0001924000005868.

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Abstract This note presents an application of algebraic methods to derive exact conditions for certain nonlinear flight dynamical systems to exhibit stability and bifurcation. The roll-coupling flight model is taken as an example to show the feasibility of algebraic analysis. Some of the previous stability and bifurcation results obtained using numerical analysis for this model are confirmed.

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26

Zahariev, E. V. "Earthquake dynamic response of large flexible multibody systems." Mechanical Sciences 4, no. 1 (2013): 131–37. http://dx.doi.org/10.5194/ms-4-131-2013.

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Abstract. In the paper dynamics of large flexible structures imposed on earthquakes and high amplitude vibrations is regarded. Precise dynamic equations of flexible systems are the basis for reliable motion simulation and analysis of loading of the design scheme elements. Generalized Newton–Euler dynamic equations for rigid and flexible bodies are applied. The basement compulsory motion realized because of earthquake or wave propagation is presented in the dynamic equations as reonomic constraints. The dynamic equations, algebraic equations and reonomic constraints compile a system of differen

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27

NIU, HONG, and QINGLING ZHANG. "GENERALIZED PREDICTIVE CONTROL FOR DIFFERENCE-ALGEBRAIC BIOLOGICAL ECONOMIC SYSTEMS." International Journal of Biomathematics 06, no. 06 (2013): 1350037. http://dx.doi.org/10.1142/s179352451350037x.

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In this paper, a nonlinear difference-algebraic system is used to model some populations with stage structure when the harvest behavior and the economic interest are considered. The stability analysis is studied at the equilibrium points. After the nonlinear difference-algebraic system is changed into a linear system with the unmodeled dynamics, a generalized predictive controller with feedforward compensator is designed to stabilize the system. Adaptive-network-based fuzzy inference system (ANFIS) is used to make the unmodeled dynamic compensated. An example illustrates the effectiveness of t

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28

MENCINGER, MATEJ, and MILAN KUTNJAK. "THE DYNAMICS OF NQ-SYSTEMS IN THE PLANE." International Journal of Bifurcation and Chaos 19, no. 01 (2009): 117–33. http://dx.doi.org/10.1142/s0218127409022786.

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The dynamics of discrete homogeneous quadratic planar maps is considered via the algebraic approach. There is a one-to-one correspondence between these systems and 2D commutative algebras (c.f. [Markus, 1960]). In particular, we consider the systems corresponding to algebras which contain some nilpotents of rank two (i.e. NQ-systems). Markus algebraic classification is used to obtain the class representatives. The case-by-case dynamical analysis is presented. It is proven that there is no chaos in NQ-systems. Yet, some cases are really interesting from the dynamical and bifurcational points of

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29

Tai, Yongpeng, Ning Chen, Lijin Wang, Zaiyong Feng, and Jun Xu. "A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control." Mathematics 8, no. 7 (2020): 1134. http://dx.doi.org/10.3390/math8071134.

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Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials. In recent years, there have been a few works about the numerical method of the fractional differential-algebraic equations. However, most of the methods cannot be directly applied in the equations of dynamic systems. This paper presents a numerical algorithm of fractional differential-algebraic equations based on the theory of sliding mode control and

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30

Fatima, Feneniche, and Rezaoui Med Salem. "Dynamics of the polynomial differential systems." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 14, no. 03 (2023): 524–35. http://dx.doi.org/10.61841/turcomat.v14i03.14069.

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31

Najdenov, Sergej, and Vladimir Yanovsky. "Geometrical nonlinear dynamics features of systems with elastic reflections." Izvestiya VUZ. Applied Nonlinear Dynamics 10, no. 1-2 (2002): 113–26. http://dx.doi.org/10.18500/0869-6632-2002-10-1-113-126.

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Within the framework оf the new geometrical-dynamic approach а special class оf dynamic systems - reversible mappings with projective involutions оп «symmetric» phase space - is linked with billiard systems. Basic geometrical features оf locally smooth billiard involutions - projectivity and piecewise discontinuity are explored and their role in making оf one оr another (regular and random) nonlinear billiard dynamics is indicated. Billiard involutions for simple algebraic curves are obtained and their common properties are set.

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32

Gorobtsov, A. S. "Dynamic balance generalized problem and the promising areas of its application." Proceedings of Higher Educational Institutions. Маchine Building, no. 3 (756) (March 2023): 14–24. http://dx.doi.org/10.18698/0536-1044-2023-3-14-24.

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The paper considers the generalized problem of the machines and mechanisms dynamic balance in terms of ensuring the given laws of altering reactions in the selected links. Representation of equations of the mechanical systems dynamics in the form of differential algebraic equations was used making it possible to obtain mathematical models of the nonlinear mechanical systems dynamics with the arbitrary structure of kinematic and force connections. With this approach, the constraint reactions are determined by algebraic equations from the system coordinates. The problem solution is based on chan

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33

Piattelli-Palmarini, Massimo, and Giuseppe Vitiello. "Linguistics and Some Aspects of Its Underlying Dynamics." Biolinguistics 9 (December 8, 2015): 096–115. http://dx.doi.org/10.5964/bioling.9033.

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In recent years, central components of a new approach to linguistics, the Minimalist Program, have come closer to physics. In this paper, an interesting and productive isomorphism is established between minimalist structure, algebraic structures, and many-body field theory opening new avenues of inquiry on the dynamics underlying some central aspects of linguistics. Features such as the unconstrained nature of recursive Merge, the difference between pronounced and un-pronounced copies of elements in a sentence, and the Fibonacci sequence in the syntactic derivation of sentence structures, are

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34

Neira-García, Jorge, Andrés Beltrán-Pulido, and John Cortés-Romero. "Algebraic Speed Estimation for Sensorless Induction Motor Control: Insights from an Electric Vehicle Drive Cycle." Electronics 13, no. 10 (2024): 1937. http://dx.doi.org/10.3390/electronics13101937.

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Induction motors (IMs) must meet high reliability and safety standards in mission-critical applications, such as electric vehicles (EVs), where sensorless control strategies are fundamental. However, sensorless rotor speed estimation demands improvements to overcome filtering distortions, tuning complexities, and sensitivity to IM model mismatch. Algebraic methods offer inherent filtering capabilities and design flexibility to address these challenges without introducing additional dynamics into the control system. The objective of this paper is to provide an algebraic estimation strategy that

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35

Batra, Anjula, and Patrick Morton. "Algebraic Dynamics of Polynomial Maps on the Algebraic Closure of a Finite Field, II." Rocky Mountain Journal of Mathematics 24, no. 3 (1994): 905–32. http://dx.doi.org/10.1216/rmjm/1181072380.

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36

Batra, Anjula, and Patrick Morton. "Algebraic Dynamics of Polynomial Maps on the Algebraic Closure of a Finite Field, I." Rocky Mountain Journal of Mathematics 24, no. 2 (1994): 453–81. http://dx.doi.org/10.1216/rmjm/1181072411.

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37

Ayasun, Saffet. "Effects of algebraic singularities on the voltage dynamics of differential-algebraic power system model." European Transactions on Electrical Power 18, no. 6 (2008): 547–61. http://dx.doi.org/10.1002/etep.209.

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38

Chatzidakis, Zoé, and Ehud Hrushovski. "Difference fields and descent in algebraic dynamics. I." Journal of the Institute of Mathematics of Jussieu 7, no. 4 (2008): 653–86. http://dx.doi.org/10.1017/s1474748008000273.

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AbstractWe draw a connection between the model-theoretic notions of modularity (or one-basedness), orthogonality and internality, as applied to difference fields, and questions of descent in in algebraic dynamics. In particular we prove in any dimension a strong dynamical version of Northcott's theorem for function fields, answering a question of Szpiro and Tucker and generalizing a theorem of Baker's for the projective line.The paper comes in three parts. This first part contains an exposition some of the main results of the model theory of difference fields, and their immediate connection to

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39

LESFARI, A., та A. ELACHAB. "THE YANG–MILLS EQUATIONS AND THE INTERSECTION OF QUARTICS IN PROJECTIVE 4-SPACE ℂℙ4". International Journal of Geometric Methods in Modern Physics 03, № 02 (2006): 201–8. http://dx.doi.org/10.1142/s0219887806001107.

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In this paper, we discuss an interesting interaction between complex algebraic geometry and dynamics: the integrability of the Yang–Mills system for a field with gauge group SU(2) and the intersection of quartics in projective 4-space ℂℙ4. Using Enriques classification of algebraic surfaces and dynamics, we show that these two quartics intesect in the affine part of an abelian surface and it follows that the system of differential equations is algebraically completely integrable.

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40

Fakhruddin, Najmuddin. "The algebraic dynamics of generic endomorphisms of ℙn". Algebra & Number Theory 8, № 3 (2014): 587–608. http://dx.doi.org/10.2140/ant.2014.8.587.

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41

Bao, Jiaqi, and Ningyuan Yao. "Definably topological dynamics of p-adic algebraic groups." Annals of Pure and Applied Logic 173, no. 4 (2022): 103077. http://dx.doi.org/10.1016/j.apal.2021.103077.

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42

Anashin, Vladimir S. "Noncommutative algebraic dynamics: Ergodic theory for profinite groups." Proceedings of the Steklov Institute of Mathematics 265, no. 1 (2009): 30–58. http://dx.doi.org/10.1134/s0081543809020035.

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43

Franz, Silvio, and Giorgio Parisi. "Quasi-equilibrium in glassy dynamics: an algebraic view." Journal of Statistical Mechanics: Theory and Experiment 2013, no. 02 (2013): P02003. http://dx.doi.org/10.1088/1742-5468/2013/02/p02003.

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44

Pawełczyk, Jacek, and Harold Steinacker. "Algebraic brane dynamics on SU(2): excitation spectra." Journal of High Energy Physics 2003, no. 12 (2003): 010. http://dx.doi.org/10.1088/1126-6708/2003/12/010.

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45

Madhavi Sastry, G., and V. Sabareesh. "The Lie-algebraic approach to hemeprotein-ligand dynamics." Chemical Physics Letters 369, no. 5-6 (2003): 691–97. http://dx.doi.org/10.1016/s0009-2614(03)00041-1.

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46

Nagul, N. V. "The logic-algebraic equations method in system dynamics." St. Petersburg Mathematical Journal 24, no. 4 (2013): 645–62. http://dx.doi.org/10.1090/s1061-0022-2013-01258-1.

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47

Emmrich, Etienne, and Volker Mehrmann. "Operator Differential-Algebraic Equations Arising in Fluid Dynamics." Computational Methods in Applied Mathematics 13, no. 4 (2013): 443–70. http://dx.doi.org/10.1515/cmam-2013-0018.

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Abstract. Existence and uniqueness of generalized solutions to initial value problems for a class of abstract differential-algebraic equations (DAEs) is shown. The class of equations covers, in particular, the Stokes and Oseen problem describing the motion of an incompressible or nearly incompressible Newtonian fluid but also their spatial semi-discretization. The equations are governed by a block operator matrix with entries that fulfill suitable inf-sup conditions. The problem data are required to satisfy appropriate consistency conditions. The results in infinite dimensions are compared in

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48

Chatzidakis, Zoé, and Ehud Hrushovski. "Difference fields and descent in algebraic dynamics. II." Journal of the Institute of Mathematics of Jussieu 7, no. 4 (2008): 687–704. http://dx.doi.org/10.1017/s1474748008000170.

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AbstractThis second part of the paper strengthens the descent theory described in the first part to rational maps and arbitrary base fields. We obtain in particular a decomposition of any difference field extension into a tower of finite, field-internal and one-based difference field extensions. This is needed in order to obtain the ‘dynamical Northcott’ Theorem 1.11 of Part I in sharp form.

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49

Tsakiris, M. C., and D. C. Tarraf. "Algebraic decompositions of DP problems with linear dynamics." Systems & Control Letters 85 (November 2015): 46–53. http://dx.doi.org/10.1016/j.sysconle.2015.09.001.

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50

De Filippo, S., G. Landi, G. Marmo, and G. Vilasi. "An algebraic description of the electron—monopole dynamics." Physics Letters B 220, no. 4 (1989): 576–80. http://dx.doi.org/10.1016/0370-2693(89)90789-2.

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