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
• Enlaces
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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.

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