The Space of Dynamical Systems with the C0-Topology

This is an introduction to the main methods and principal results in the theory of Ca-small perturbations of dynamical systems. It is the first comprehensive treatment of this topic. In particular, Ca-generic properties of dynamical systems, topological stability, perturbations of attractors, and limit sets of domains are discussed. The book contains such new results as Lipschitz shadowing of pseudotrajectories in structurally stable diffeo-morphisms. The aim of the author was to simplify basic proofs, so that the main part of the book would be accessible to graduate students in pure and applied mathematics. The book has also been designed as a basic reference for researchers in various fields of dynamical systems and their applications, especially for those who study attractors or pseudotrajectories generated by numerical methods.