English

On zero entropy homeomorphisms of the pseudo-arc

Dynamical Systems 2024-09-11 v2 General Topology

Abstract

In this paper we study interval maps ff with zero topological entropy that are crooked; i.e. whose inverse limit with ff as the single bonding map is the pseudo-arc. We show that there are uncountably many pairwise non-conjugate zero entropy crooked interval maps with different sets of fixed points. We also show that there are uncountably many zero entropy crooked maps that are pairwise non-conjugate and have exactly two fixed points. Furthermore, we provide a characterization of crooked interval maps that are under or above the identity diagonal.

Keywords

Cite

@article{arxiv.2405.20533,
  title  = {On zero entropy homeomorphisms of the pseudo-arc},
  author = {Jernej Činč},
  journal= {arXiv preprint arXiv:2405.20533},
  year   = {2024}
}

Comments

Accepted version; former Section 4 shortened and became Example 3.6, some typos corrected