Nikolay Kuznetsov

(Author)

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation: Dedicated to Gennady Leonov (2021)Hardcover - 2021, 3 July 2020

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation: Dedicated to Gennady Leonov (2021)
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Part of Series
Emergence, Complexity and Computation
Print Length
545 pages
Language
English
Publisher
Springer
Date Published
3 Jul 2020
ISBN-10
3030509869
ISBN-13
9783030509866

Description

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.

Product Details

Authors:
Nikolay KuznetsovVolker Reitmann
Book Edition:
2021
Book Format:
Hardcover
Country of Origin:
NL
Date Published:
3 July 2020
Dimensions:
23.39 x 15.6 x 3.18 cm
ISBN-10:
3030509869
ISBN-13:
9783030509866
Language:
English
Location:
Cham
Pages:
545
Publisher:
Weight:
966.15 gm

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