On the Entropy of Flows with Reparametrized Gluing Orbit Property

TL;DR

This paper proves that flows with a reparametrized gluing orbit property are either minimal or have positive topological entropy, revealing a dichotomy in their dynamical complexity.

Contribution

It introduces a weaker reparametrized gluing orbit property and establishes a dichotomy between minimality and positive entropy for such flows.

Findings

Flows with the reparametrized gluing orbit property are either minimal or have positive entropy.

The work characterizes the dynamical complexity of flows under a weaker orbit property.

Provides a new perspective on the relationship between orbit properties and entropy.

Abstract

We show that a flow or a semiflow with a weaker reparametrized form of gluing orbit property is either minimal or of positive topological entropy.