Dynamics of topological flows and homeomorphisms with a finite hyperbolic chain-recurrent set on n-dimensional manifolds
Starting from dimension 4, so-called non-smoothed manifolds, manifolds that do not allow triangulation and other obstacles that prevent the use of the technique of smooth manifolds for the study of multidimensional manifolds appear. In addition, all methods for studying smooth dynamical systems on multidimensional manifolds are based on the approximation of all subsets by piecewise linear or topological objects. In this regard, the idea of consideration of dynamical systems on multidimensional manifolds that do not use the concept of smoothness in their definition is completely natural. So homeomorphisms and topological Morse-Smale flows, which are also firmly connected with the topology of the ambient manifold, as well as their smooth analogues, have already entered into scientific usage. In the present paper we investigate general dynamical properties of homeomorphisms and topological flows with a finite hyperbolic chain recurrent set.