On Zero Entropy Homeomorphisms of the Pseudo-arc

Jernej Cinc ^[1]
1. [1] University of Maribor
  
  University of Maribor
  
  Eslovenia
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
Idioma: inglés
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Resumen
- 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 zero entropy pairwise non-conjugate zero entropy crooked interval maps with different sets of fixed points. We also show that there are uncountably many 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 diagonal.