Minimal non-invertible maps on the pseudo-circle

TL;DR

This paper proves that the pseudo-circle admits a minimal non-invertible map, resolving a longstanding open problem using advanced topological techniques and detailed structural analysis.

Contribution

It demonstrates the existence of minimal non-invertible maps on the pseudo-circle, a problem previously unresolved in topological dynamics.

Findings

Pseudo-circle admits a minimal non-invertible map

Resolved a problem posed by Bruin, Kolyada, and Snoha

Utilized Denjoy-Rees technique and structural analysis

Abstract

In this article, we show that R.H. Bing's pseudo-circle admits a minimal non-invertible map. This resolves a problem raised by Bruin, Kolyada and Snoha in the negative. The main tool is the Denjoy-Rees technique, further developed by B\'eguin-Crovisier-Le Roux, combined with detailed study into the structure of the pseudo-circle.