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arXiv · 2405.20533

On zero entropy homeomorphisms of the pseudo-arc

Jernej Činč
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Abstract

In this paper we study interval maps $f$ with zero topological entropy that are crooked; i.e. whose inverse limit with $f$ 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.

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Jernej Činč. 2024-05-30. On zero entropy homeomorphisms of the pseudo-arc. https://arxiv.org/abs/2405.20533

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