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Relevant bibliographies by topics / Bernoulli systems

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Academic literature on the topic 'Bernoulli systems'

Author: Grafiati

Published: 14 December 2024

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Journal articles on the topic "Bernoulli systems"

1

GERBER, MARLIES, and PHILIPP KUNDE. "Loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli." Ergodic Theory and Dynamical Systems 42, no. 3 (2021): 917–73. http://dx.doi.org/10.1017/etds.2021.73.

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AbstractForeman and Weiss [Measure preserving diffeomorphisms of the torus are unclassifiable. Preprint, 2020, arXiv:1705.04414] obtained an anti-classification result for smooth ergodic diffeomorphisms, up to measure isomorphism, by using a functor $\mathcal {F}$ (see [Foreman and Weiss, From odometers to circular systems: a global structure theorem. J. Mod. Dyn.15 (2019), 345–423]) mapping odometer-based systems, $\mathcal {OB}$ , to circular systems, $\mathcal {CB}$ . This functor transfers the classification problem from $\mathcal {OB}$ to $\mathcal {CB}$ , and it preserves weakly mixing extensions, compact extensions, factor maps, the rank-one property, and certain types of isomorphisms. Thus it is natural to ask whether $\mathcal {F}$ preserves other dynamical properties. We show that $\mathcal {F}$ does not preserve the loosely Bernoulli property by providing positive and zero-entropy examples of loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli. We also construct a loosely Bernoulli circular system whose corresponding odometer-based system has zero entropy and is not loosely Bernoulli.

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2

Chernov, N. I., and C. Haskell. "Nonuniformly hyperbolic K-systems are Bernoulli." Ergodic Theory and Dynamical Systems 16, no. 1 (1996): 19–44. http://dx.doi.org/10.1017/s0143385700008695.

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AbstractWe prove that those non-uniformly hyperbolic maps and flows (with singularities) that enjoy the K-property are also Bernoulli. In particular, many billiard systems, including those systems of hard balls and stadia that have the K-property, and hyperbolic billiards, such as the Lorentz gas in any dimension, are Bernoulli. We obtain the Bernoulli property for both the billiard flows and the associated maps on the boundary of the phase space.

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3

Filipovic, Mirjana. "New form of the Euler-Bernoulli rod equation applied to robotic systems." Theoretical and Applied Mechanics 35, no. 4 (2008): 381–406. http://dx.doi.org/10.2298/tam0804381f.

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This paper presents a theoretical background and an example of extending the Euler-Bernoulli equation from several aspects. Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. The stiffness matrix is a full matrix. Damping is an omnipresent elasticity characteristic of real systems, so that it is naturally included in the Euler-Bernoulli equation. It is shown that Daniel Bernoulli's particular integral is just one component of the total elastic deformation of the tip of any mode to which we have to add a component of the elastic deformation of a stationary regime in accordance with the complexity requirements of motion of an elastic robot system. The elastic line equation mode of link of a complex elastic robot system is defined based on the so-called 'Euler-Bernoulli Approach' (EBA). It is shown that the equation of equilibrium of all forces present at mode tip point ('Lumped-mass approach' (LMA)) follows directly from the elastic line equation for specified boundary conditions. This, in turn, proves the essential relationship between LMA and EBA approaches. In the defined mathematical model of a robotic system with multiple DOF (degree of freedom) in the presence of the second mode, the phenomenon of elasticity of both links and joints are considered simultaneously with the presence of the environment dynamics - all based on the previously presented theoretical premises. Simulation results are presented. .

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4

ORNSTEIN, DONALD, and BENJAMIN WEISS. "On the Bernoulli nature of systems with some hyperbolic structure." Ergodic Theory and Dynamical Systems 18, no. 2 (1998): 441–56. http://dx.doi.org/10.1017/s0143385798100354.

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It is shown that systems with hyperbolic structure have the Bernoulli property. Some new results on smooth cross-sections of hyperbolic Bernoulli flows are also derived. The proofs involve an abstract version of our original methods for showing that the geodesic flow on surfaces of negative curvature are Bernoulli.

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5

LIAO, GANG, WENXIANG SUN, EDSON VARGAS, and SHIROU WANG. "Approximation of Bernoulli measures for non-uniformly hyperbolic systems." Ergodic Theory and Dynamical Systems 40, no. 1 (2018): 233–47. http://dx.doi.org/10.1017/etds.2018.33.

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An invariant measure is called a Bernoulli measure if the corresponding dynamics is isomorphic to a Bernoulli shift. We prove that for$C^{1+\unicode[STIX]{x1D6FC}}$diffeomorphisms any weak mixing hyperbolic measure could be approximated by Bernoulli measures. This also holds true for$C^{1}$diffeomorphisms preserving a weak mixing hyperbolic measure with respect to which the Oseledets decomposition is dominated.

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6

DOOLEY, A. H., V. YA GOLODETS, D. J. RUDOLPH, and S. D. SINEL’SHCHIKOV. "Non-Bernoulli systems with completely positive entropy." Ergodic Theory and Dynamical Systems 28, no. 1 (2008): 87–124. http://dx.doi.org/10.1017/s014338570700034x.

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AbstractA new approach to actions of countable amenable groups with completely positive entropy (cpe), allowing one to answer some basic questions in this field, was recently developed. The question of the existence of cpe actions which are not Bernoulli was raised. In this paper, we prove that every countable amenable groupG, which contains an element of infinite order, has non-Bernoulli cpe actions. In fact we can produce, for any$h \in (0, \infty ]$, an uncountable family of cpe actions of entropyh, which are pairwise automorphically non-isomorphic. These actions are given by a construction which we call co-induction. This construction is related to, but different from the standard induced action. We study the entropic properties of co-induction, proving that ifαGis co-induced from an actionαΓof a subgroup Γ, thenh(αG)=h(αΓ). We also prove that ifαΓis a non-Bernoulli cpe action of Γ, thenαGis also non-Bernoulli and cpe. Hence the problem of finding an uncountable family of pairwise non-isomorphic cpe actions of the same entropy is reduced to one of finding an uncountable family of non-Bernoulli cpe actions of$\mathbb Z$, which pairwise satisfy a property we call ‘uniform somewhat disjointness’. We construct such a family using refinements of the classical cutting and stacking methods.

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7

Barbieri, Giuseppina, and Giacomo Lenzi. "Entropy of MV-algebraic dynamical systems: An example." Mathematica Slovaca 69, no. 2 (2019): 267–74. http://dx.doi.org/10.1515/ms-2017-0221.

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Abstract We give examples showing that the Kolmogorov-Sinai entropy generator theorem is false for both upper and lower Riesz entropy of MV-algebraic dynamical systems, both two sided (i.e., analogous to two sided Bernoulli shifts) and one sided (i.e., analogous to one sided Bernoulli shifts).

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8

Nicol, Matthew. "Induced maps of hyperbolic Bernoulli systems." Discrete & Continuous Dynamical Systems - A 7, no. 1 (2001): 147–54. http://dx.doi.org/10.3934/dcds.2001.7.147.

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9

Beebee, John. "Bernoulli Numbers and Exact Covering Systems." American Mathematical Monthly 99, no. 10 (1992): 946. http://dx.doi.org/10.2307/2324488.

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10

Akaishi, A., M. Hirata, K. Yamamoto, and A. Shudo. "Meeting time distributions in Bernoulli systems." Journal of Physics A: Mathematical and Theoretical 44, no. 37 (2011): 375101. http://dx.doi.org/10.1088/1751-8113/44/37/375101.

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