On minimal manifolds

TL;DR

This paper proves that any compact manifold of dimension at least 2 that admits a minimal homeomorphism also admits a minimal noninvertible map, expanding understanding of minimal dynamics on manifolds.

Contribution

It establishes the existence of minimal noninvertible maps on manifolds that already support minimal homeomorphisms, revealing new dynamical possibilities.

Findings

Existence of minimal noninvertible maps on certain manifolds

Extension of minimal dynamics from invertible to noninvertible maps

Broader class of manifolds supporting minimal dynamics

Abstract

Let $M$ be a compact manifold of dimension at least 2. If $M$ admits a minimal homeomorphism then $M$ admits a minimal noninvertible map.