Various notions of topological transitivity in non-autonomous and generic dynamical systems

TL;DR

This paper explores different notions of topological transitivity in non-autonomous and generic dynamical systems, providing equivalences and relationships between these notions in both system types.

Contribution

It introduces new conditions and implications for transitivity in NDDS and GDS, and examines their interconnections and equivalences.

Findings

Many equivalent conditions for transitivity notions.

Implications among transitivity notions in NDDS and GDS.

Relationship between transitivity variations in NDDS and associated GDS.

Abstract

We consider two types of dynamical systems namely non-autonomous discrete dynamical systems(NDDS) and generic dynamical systems(GDS). In both of them, we study various notions of transitivity. We give many equivalent conditions for each of these notions and present the implications among these in NDDS and GDS. For a given NDDS, we associate a GDS and discuss whether if the given NDDS has a particular variation of transitivity then the associated GDS also has such a variation and vice versa.