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Emergence, Complexity and Computation

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

Dedicated to Gennady Leonov

Authors: Kuznetsov, Nikolay, Reitmann, Volker

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  • Provides a systematic presentation of research activities in the dimension theory of dynamical systems in finite-dimensional Euclidean spaces and manifolds
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  • Investigates global attractors and invariant sets for dynamical systems by means of Lyapunov functions and adapted metrics
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  • Presents theory and simulations on attractor dimension estimates for dynamical systems
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  • ISBN 978-3-030-50987-3
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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.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $149.00
price for USA in USD
  • ISBN 978-3-030-50987-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-3-030-50986-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Attractor Dimension Estimates for Dynamical Systems: Theory and Computation
Book Subtitle
Dedicated to Gennady Leonov
Authors
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

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