Authors:
- Provides a systematic presentation of research activities in the dimension theory of dynamical systems in finite-dimensional Euclidean spaces and manifolds
- Investigates global attractors and invariant sets for dynamical systems by means of Lyapunov functions and adapted metrics
- Presents theory and simulations on attractor dimension estimates for dynamical systems
Part of the book series: Emergence, Complexity and Computation (ECC, volume 38)
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Table of contents (10 chapters)
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Front Matter
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Basic Elements of Attractor and Dimension Theories
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Front Matter
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Dimension Estimates for Almost Periodic Flows and Dynamical Systems in Euclidean Spaces
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Front Matter
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Dimension Estimates on Riemannian Manifolds
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Front Matter
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Back Matter
About this book
This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.
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Authors and Affiliations
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Department of Applied Cybernetics, Faculty of Mathematics and Mechanics, St. Petersburg State University, St.Petersburg, Russia
Nikolay Kuznetsov
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Department of Applied Cybernetics, Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
Volker Reitmann
Bibliographic Information
Book Title: Attractor Dimension Estimates for Dynamical Systems: Theory and Computation
Book Subtitle: Dedicated to Gennady Leonov
Authors: Nikolay Kuznetsov, Volker Reitmann
Series Title: Emergence, Complexity and Computation
DOI: https://doi.org/10.1007/978-3-030-50987-3
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-50986-6Published: 03 July 2020
Softcover ISBN: 978-3-030-50989-7Published: 03 July 2021
eBook ISBN: 978-3-030-50987-3Published: 02 July 2020
Series ISSN: 2194-7287
Series E-ISSN: 2194-7295
Edition Number: 1
Number of Pages: XIX, 545
Number of Illustrations: 24 b/w illustrations, 10 illustrations in colour
Topics: Theory of Computation, Applications of Nonlinear Dynamics and Chaos Theory, Complex Systems