# Recurrence in generalized semigroup

## TL;DR

This paper extends classical dynamical concepts like recurrence, periodicity, and nonwandering points to the setting of generalized semigroups on topological spaces, establishing their interrelations.

## Contribution

It introduces and analyzes generalized notions of recurrence, periodic points, and nonwandering points within semigroup dynamics, broadening classical dynamical systems theory.

## Key findings

- Established relationships between generalized recurrence notions
- Extended classical concepts to semigroup settings
- Provided foundational framework for future research

## Abstract

In [arXiv:1904.12333], we introduced the concept of escaping set in general setting for a topological space and extended the notion of limit set and escaping set for the general semigroup generated by continuous self maps. In this paper we continue with extending the other notions of recurrence for the generalized semigroup analogs to their counterpart in the classical theory of dynamics. We discuss the concept of periodic point, nonwandering point and chain recurrent point in the more general setting of a semigroup and establish the correlation between them.