Title: Attractor Dimension Estimates for Dynamical Systems: Theory and Computation: Dedicated to Gennady Leonov (Emergence, Complexity and Computation, 38)
Publisher: Springer
Publication Date: 2021
Language: English
ISBN 10: 3030509893
ISBN 13: 9783030509897
Binding: Soft cover
Condition: New

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Synopsis

This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carath�odory 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 H�non 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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