On topological classification of \(A\)-diffeomorphisms of surfaces (Q1570902)

This paper is a review of results obtained by the author and related to the topological classification of discrete dynamical systems (cascades) defined on an orientable smooth closed surface \({\mathcal A}_g\) of genus \(g\geq 0\). Topics are: 1) topological classification of one-dimensional basic sets via automorphisms of fundamental groups, 2) representation of one-dimensional basic sets by hyperbolic homeomorphisms, 3) structural stability and asymptotic behaviour of invariant manifolds of \(A\)-diffeomorphisms, 4) topological classification of Morse-Smale diffeomorphisms with a finite set of heteroclinic trajectories, 5) topological classification of structurally stable diffeomorphisms with one-dimensional basic sets.