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Attractor Dimension Estimates for Dynamical Systems: Theory and Computation: Dedicated to Gennady Leonov: 38 (Emergence, Complexity and Computation, 38) - Hardcover

Book 37 of 47: Emergence, Complexity and Computation

Kuznetsov, Nikolay; Reitmann, Volker

 
9783030509866: Attractor Dimension Estimates for Dynamical Systems: Theory and Computation: Dedicated to Gennady Leonov: 38 (Emergence, Complexity and Computation, 38)
Hardcover
ISBN 10: 3030509869 ISBN 13: 9783030509866
Publisher: Springer, 2020

Synopsis

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2020
Language
English
ISBN 10 
3030509869
ISBN 13 
9783030509866
Binding
Hardcover
Edition number
1
Number of pages
564