Attractor dimension estimates for dynamical systems : theory and computation : dedicated to Gennady Leonov / Nikolay Kuznetsov, Volker Reitmann.
Kuznetsov, Nikolay.; Reitmann, Volker, 1948-
2021
QA614.813
Available Online

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Title Attractor dimension estimates for dynamical systems : theory and computation : dedicated to Gennady Leonov / Nikolay Kuznetsov, Volker Reitmann.
Author Kuznetsov, Nikolay.
ISBN 9783030509873 (electronic bk.)
3030509877 (electronic bk.)
3030509869
9783030509866
DOI https://doi.org/10.1007/978-3-030-50987-3.
Imprint Cham : Springer, [2021]
Language English
Description 1 online resource
Other Standard Identifiers 10.1007/978-3-030-50987-3. doi
10.1007/978-3-030-50
Call Number QA614.813
Dewey Decimal Classification 515/.39
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Added Author Reitmann, Volker, 1948-
Series Emergence, complexity and computation ; 38.
Available in Other Form Attractor dimension estimates for dynamical systems.
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Attractors and Lyapunov Functions
Singular Values, Exterior Calculus and Logarithmic Norms
Introduction to Dimension Theory.

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