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Attractors and Lyapunov Functions

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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

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.

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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). Attractors and Lyapunov Functions. 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_1

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  • DOI: https://doi.org/10.1007/978-3-030-50987-3_1

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  • Online ISBN: 978-3-030-50987-3

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