Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

This book provides analytical and numerical methods for the estimation of dimensioncharacteristics (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 usingestimates based on Lyapunov functions and adapted metrics.Moreover, itintroducesvarious types of Lyapunov dimensions of dynamical systems with respect to an invariant set,based on local,global and uniform Lyapunov exponents, andderivesanalytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems.Lastly, the bookpresentsestimates 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.