2024/05/30 by Jernej Činč, Činč, Jernej
Computer Science · #37B45 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Fuzzy Logic and Control Systems #General Topology (math.GN) #Neural Networks and Applications #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2405.20533
openalex publication_date 2024/05/30 · openalex created_date 2024/06/07 · openalex updated_date 2026/07/28
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.