Attractor Dimension Estimates for Dynamical Systems: Theory 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.

Provides a systematic presentation of research activities in the dimension theory of dynamical systems in finite-dimensional Euclidean spaces and manifolds Investigates global attractors and invariant sets for dynamical systems by means of Lyapunov functions and adapted metrics Presents theory and simulations on attractor dimension estimates for dynamical systems

Zusammenfassung
"It is interesting and very well written. Mostly, chapters are self-contained and rich of detailed explanations. Many powerful computational tools and algorithms provide a solid numerical background for the study of attractor dimensions. ... this book contains advanced material on attractor dimension estimates for dynamical systems. This is definitely suitable for researchers in applied mathematics and computational theory of dynamical systems." (Mohammad Sajid, zbMATH 1483.37001, 2022)

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