Controlled shadowing property

Abstract

In this paper we introduce a new notion, named controlled shadowing property and we relate it to some notions in dynamical systems such as topological ergodicity, topologically mixing and specication properties. The relation between the controlled shadowing and chaos in sense of Li-Yorke is studied. At the end we give some examples to investigate the controlled shadowing property.

Keywords

• controlled shadowing property
• chaos
• topologically ergodic
• specification property
• topologically mixing