Attractor Dimension Estimates for Dynamical Systems: Theory and Computation
Dedicated to Gennady Leonov
Authors: Kuznetsov, Nikolay, Reitmann, Volker
Free Preview- 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
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- About this book
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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.
- Table of contents (10 chapters)
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Attractors and Lyapunov Functions
Pages 3-40
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Singular Values, Exterior Calculus and Logarithmic Norms
Pages 41-93
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Introduction to Dimension Theory
Pages 95-146
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Dimensional Aspects of Almost Periodic Dynamics
Pages 149-190
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Dimension and Entropy Estimates for Dynamical Systems
Pages 191-256
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Attractor Dimension Estimates for Dynamical Systems: Theory and Computation
- Book Subtitle
- Dedicated to Gennady Leonov
- Authors
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- Nikolay Kuznetsov
- Volker Reitmann
- Series Title
- Emergence, Complexity and Computation
- Series Volume
- 38
- Copyright
- 2021
- Publisher
- Springer International Publishing
- Copyright Holder
- The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-50987-3
- DOI
- 10.1007/978-3-030-50987-3
- Hardcover ISBN
- 978-3-030-50986-6
- Series ISSN
- 2194-7287
- Edition Number
- 1
- Number of Pages
- XIX, 545
- Number of Illustrations
- 24 b/w illustrations, 10 illustrations in colour
- Topics
