On zero entropy homeomorphisms of the pseudo-arc
Dynamical Systems
2024-09-11 v2 General Topology
Abstract
In this paper we study interval maps with zero topological entropy that are crooked; i.e. whose inverse limit with 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.
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