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Attractor Dimension Estimates for Dynamical Systems: Theory and ComputationAttractors and Lyapunov Functions

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation: Attractors and... [The main tool in estimating dimensions of invariant sets and entropies of dynamical systems developed in this book is based on Lyapunov functions. In this chapter we introduce the basic concept of global attractors. The existence of a global attractor for a dynamical system follows from the dissipativity of the system. In order to show the last property we use Lyapunov functions. In this chapter we also consider some applications of Lyapunov functions to stability problems of the Lorenz system. A central result is the existence of homoclinic orbits in the Lorenz system for certain parameters.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Attractor Dimension Estimates for Dynamical Systems: Theory and ComputationAttractors and Lyapunov Functions

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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
3 –40
DOI
10.1007/978-3-030-50987-3_1
Publisher site
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Abstract

[The main tool in estimating dimensions of invariant sets and entropies of dynamical systems developed in this book is based on Lyapunov functions. In this chapter we introduce the basic concept of global attractors. The existence of a global attractor for a dynamical system follows from the dissipativity of the system. In order to show the last property we use Lyapunov functions. In this chapter we also consider some applications of Lyapunov functions to stability problems of the Lorenz system. A central result is the existence of homoclinic orbits in the Lorenz system for certain parameters.]

Published: Jul 2, 2020

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