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2021 | OriginalPaper | Buchkapitel

5. Dimension and Entropy Estimates for Dynamical Systems

verfasst von : Nikolay Kuznetsov, Volker Reitmann

Erschienen in: Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

Verlag: Springer International Publishing

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Abstract

In the present chapter various approaches to estimate the fractal dimension and the Hausdorff dimension, which involve Lyapunov functions, are developed. One of the main results of this chapter is a theorem called by us the limit theorem for the Hausdorff measure of a compact set under differentiable maps. One of the sections of Chap. 5 is devoted to applications of this theorem to the theory of ordinary differential equations. The use of Lyapunov functions in the estimates of fractal dimension and of topological entropy is also considered. The representation is illustrated by examples of concrete systems.

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Titel: Dimension and Entropy Estimates for Dynamical Systems
verfasst von: Nikolay Kuznetsov
Volker Reitmann
Verlag: Springer International Publishing
Buch: Attractor Dimension Estimates for Dynamical Systems: Theory and Computation
Print ISBN: 978-3-030-50986-6

Electronic ISBN: 978-3-030-50987-3

Copyright-Jahr: 2021
DOI: https://doi.org/10.1007/978-3-030-50987-3_5

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