Fitting shadowing property

Abstract EN

The aim of this paper is to introduce the notion of the fitting shadowing property (FSP) for a continuous map and investigate the relation between the fitting shadowing property and average shadowing property(ASP).

Let M be a metric space , ɸ : M→M be a map, we prove that if ф has the fitting shadowing property, then ˆn and͜(ф× ф× ф×… ×ф) (n-times) have the fitting shadowing property for every , also, we prove that if ф has the fitting shadowing property and the minimal points of ф are dense in , then ф is weakly mixing and totally strongly ergodic.

Finally, we obtain that if ф is surjective and has the fitting shadowing property, then ф is chain mixing.