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Attractor Dimension Estimates for Dynamical Systems: Theory and ComputationDimension and Entropy Estimates for Dynamical Systems

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation: Dimension and... [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Attractor Dimension Estimates for Dynamical Systems: Theory and ComputationDimension and Entropy Estimates for Dynamical Systems

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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-50986-6
Pages
191 –256
DOI
10.1007/978-3-030-50987-3_5
Publisher site
See Chapter on Publisher Site

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.]

Published: Jul 2, 2020

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