Attractor Dimension Estimates for Dynamical Systems : Theory and Computation
Year of publication
2020
Authors
Kuznetsov, Nikolay; Reitmann, Volker
Abstract
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.
Show moreOrganizations and authors
University of Jyväskylä
Kuznetsov Nikolay
Publication type
Publication format
Monograph
Audience
Scientific
Peer-reviewed
Peer-Reviewed
MINEDU's publication type classification code
C1 Scientific bookPublication channel information
Publisher
ISSN
ISBN
Publication forum
Publication forum level
2
Open access
Open access in the publisher’s service
No
Self-archived
No
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object],[object Object],[object Object]
Publication country
Switzerland
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.1007/978-3-030-50987-3
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes