Introduction to the topological classification of cascades on manifolds with dimension two and three

This book is an introduction to topological classification of smooth cascades with hyperbolic nonwandering set which are given on closed orientable manifolds with dimension two and three. It contains the results obtained by the authors recently, in collaboration with Russian and French mathematicians. The focus is on the solution of fundamental problems associated with non-trivial effects that distinguish discrete dynamical systems from the corresponding flows. The book provides an overview of information from the qualitative theory of dynamical systems and related disciplines, allowing to study the book almost autonomously. It will be useful for undergraduate students, graduate students and researchers, interested in the theory of dynamical systems.