C1 Book
Attractor Dimension Estimates for Dynamical Systems : Theory and Computation (2020)
Kuznetsov, N., & Reitmann, V. (2020). Attractor Dimension Estimates for Dynamical Systems : Theory and Computation. Springer. Emergence, Complexity and Computation, 38. https://doi.org/10.1007/978-3-030-50987-3
JYU authors or editors
Publication details
All authors or editors: Kuznetsov, Nikolay; Reitmann, Volker
ISBN: 978-3-030-50986-6
eISBN: 978-3-030-50987-3
Journal or series: Emergence, Complexity and Computation
ISSN: 2194-7287
eISSN: 2194-7295
Publication year: 2020
Number in series: 38
Number of pages in the book: 545
Publisher: Springer
Place of Publication: Cham
Publication country: Switzerland
Publication language: English
DOI: https://doi.org/10.1007/978-3-030-50987-3
Publication open access: Not open
Publication channel open access:
Additional information: Dedicated to Gennady Leonov.
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.
Keywords: dynamical systems; attractors; dimension; manifolds (mathematics)
Free keywords: attractor theory; dimension theory; dynamical systems; Riemannian manifolds; complex systems
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 2
