Expansivity and Shadowing for Group Actions of Some Abelian Groups and Some Finitely Generated

Abstract

For actions of finitely formed groups, we define the term "shadowing property" and examine its core attributes in the first part of this research. The development and application of a shadowing lemma for nilpotent group behavior follows. The topic of expansivity and shadowing for finitely generated group actions on metric spaces is discussed in the second section. Additionally, we demonstrate that expansivity for such an action is identical to the action having a generator. We research the chain recurrent set for shadowing actions. We discuss the difficulties with projecting and lifting for actions with expansivity and shadowing. In addition, we study shadowing properties of continuous actions of the groups.