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Dimension and Entropy Estimates for Dynamical Systems

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Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 38))

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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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Authors and Affiliations

  1. Department of Applied Cybernetics, Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

    Nikolay Kuznetsov & Volker Reitmann

  2. Faculty of Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Nikolay Kuznetsov

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  1. Nikolay Kuznetsov
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  2. Volker Reitmann
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Correspondence to Nikolay Kuznetsov .

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Kuznetsov, N., Reitmann, V. (2021). Dimension and Entropy Estimates for Dynamical Systems. In: Attractor Dimension Estimates for Dynamical Systems: Theory and Computation. Emergence, Complexity and Computation, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-030-50987-3_5

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  • DOI: https://doi.org/10.1007/978-3-030-50987-3_5

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