On N-Distal Homeomorphisms

TL;DR

This paper explores the properties of N-distal homeomorphisms, examining their behavior under factors and their relation to other dynamical concepts, and shows that N-distal systems have zero topological entropy under certain conditions.

Contribution

It introduces and analyzes the N-distal property for homeomorphisms, including its behavior under factor maps and its connection to transitivity, N-equicontinuity, and expansivity.

Findings

N-distal systems have zero topological entropy on compact metric spaces.

The paper establishes relationships between N-distality and transitivity, N-equicontinuity, and expansivity.

Behavior of N-distal systems under factor operations is characterized.

Abstract

In this work we exploit the notion of N-distal property for a homeomorphisms. We study how it behaves under factor operations. We investigate the relation between N-distality and transitivity, N-equicontinuity and expansivity. We also prove that topological topological entropy vanishes for N-distal systems on compact metric spaces with some nice behavior on the non-wandering set.