Topological chain and shadowing properties of dynamical systems on uniform spaces

This paper discusses topological shadowing property, chain transitivity, total chain transitivity, and chain mixing property for dynamical systems on uniform spaces and characterizes some topological chain properties for dynamical systems on compact uniform spaces. In particular, it is proved that a compact dynamical system is topologically chain mixing if and only if it is totally topologically chain transitive. Moreover, some basic properties of topological shadowing and non-wandering points on uniform spaces are obtained.