On Zero Entropy Homeomorphisms of the Pseudo-arc

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.