Chaotic behaviour of maps possessing the almost average shadowing property

Abstract

In this paper, we investigate the chaotic behaviour of maps having the almost average shadowing property by obtaining the relationship of the almost average shadowing property with different kinds of chaos. Moreover, we relate the notion of almost average shadowing property with some other types of shadowing properties, for instance, ergodic shadowing, $\mathcal{F}_{\underline{d}}$-shadowing and $\underline{d}$-shadowing. We also study the notion of almost average shadowing property for maps induced on hyperspaces. Our study is supported by providing counter-examples wherever necessary.