English

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

Dynamical Systems 2025-05-12 v3 General Topology

Abstract

We prove the entropy conjecture of M. Barge from 1989: for every r[0,]r\in [0,\infty] there exists a pseudo-arc homeomorphism hh, whose topological entropy is rr. Until now all pseudo-arc homeomorphisms with known entropy have had entropy 00 or \infty.

Keywords

Cite

@article{arxiv.2105.11133,
  title  = {Beyond $0$ and $\infty$: A solution to the Barge Entropy Conjecture},
  author = {Jan P. Boroński and Jernej Činč and Piotr Oprocha},
  journal= {arXiv preprint arXiv:2105.11133},
  year   = {2025}
}

Comments

Revised version of the paper, following referee reports

R2 v1 2026-06-24T02:23:50.804Z