Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

Dedicated to Gennady Leonov
1. Auflage 2021
ISBN: 978-3-030-50989-7
Verlag: Springer International Publishing

Buch, Englisch, Band 38, 545 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 850 g

Reihe: Emergence, Complexity and Computation

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.

Zielgruppe

Research

Autoren/Hrsg.

Reitmann, Volker

Kuznetsov, Nikolay

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme

Inhaltsverzeichnis

Attractors and Lyapunov Functions.- Singular Values, Exterior Calculus and Logarithmic Norms.- Introduction to Dimension Theory.