Titlebook: Ergodic Theory and Dynamical Systems; Yves Coudène Textbook 2016 Springer-Verlag London 2016 Ergodic theory.Dynamical systems.Hyperbolic d

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A Strange AttractorUsing the Hartman–Grobman theorem, we can show that a small perturbation . of a hyperbolic toral automorphism is conjugate to this automorphism. For such a transformation, all points are therefore nonwandering, and there exists a dense set of recurrent points.

Wallow

EntropyLet us study the problem of conjugation from the measure-theoretic viewpoint. Consider two measure-preserving dynamical systems given by a map ..: .. → .. preserving a measure .. and a map ..: .. → .. preserving a measure ...

orthodox

Computing EntropyIn general, computing the entropy of a measure-preserving transformation is a delicate problem. We will study a class of noninvertible maps for which the computation does not present too many problems.

Ligneous

Measurable Partitions and ,-AlgebrasThis chapter studies the notion of measurable partition in detail. As far as we know, there exists no elementary treatise of this notion, and yet it plays an important role in ergodic theory. We have seen it play a role in Chap. . when we studied the decomposition of a transformation into ergodic components.

肌肉

https://doi.org/10.1007/978-981-99-2209-3 finite measure . representing an extensive quantity conserved during the motion. We wish to study the sequence {..(.)}., which represents the succession of states the system takes on over time. This sequence makes up the . of the point ., or its ..

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Mikroorganismen im Dienst der Umwelt,e development of thermodynamics and statistical mechanics with the work of J.W. Gibbs and L. Boltzmann at the end of the nineteenth century. It was, however, not these two theories that inspired A.N. Kolmogorov when he introduced a new invariant called “entropy” to study dynamical systems, but rather the work of C.E. Shannon on information theory.

遗传

Bioinspired Self-cleaning Materials,r having dismissed a negligible set of points in both spaces, we can find a measure-preserving measurable bijection whose inverse is also measurable. If two dynamical systems are isomorphic, so are their underlying spaces.

终点

https://doi.org/10.1007/978-3-030-93333-3hese pieces. We call this a .. The number of components may be uncountable, but the resulting partition still satisfies a certain regularity property: it is possible to approximate it with partitions having finitely many pieces.

丰富

BAIL

Entropy and Information Theorye development of thermodynamics and statistical mechanics with the work of J.W. Gibbs and L. Boltzmann at the end of the nineteenth century. It was, however, not these two theories that inspired A.N. Kolmogorov when he introduced a new invariant called “entropy” to study dynamical systems, but rather the work of C.E. Shannon on information theory.