Beyond $0$ and $\infty$: A solution to the Barge Entropy Conjecture

Abstract

We prove the entropy conjecture of M. Barge from 1989: for every $r\in [0,\infty ]$ there exists a pseudo-arc homeomorphism $h$, whose topological entropy is $r$. Until now all pseudo-arc homeomorphisms with known entropy have had entropy $0$ or $\infty$.

Revised version of the paper, following referee reports

References in corpus (2)

• Arc-like continua, Julia sets of entire functions, and Eremenko's Conjecture
• New exotic minimal sets from pseudo-suspensions of Cantor systems