Topological sequence entropy and topological dynamics of tree maps

Aymen Daghar, Jose S. Canovas

Published 2022-04-27Version 1

We prove that a zero topological entropy continuous tree map always displays zero topological sequence entropy when it is restricted to its non-wandering and chain recurrent sets. In addition, we show that a similar result is not possible when the phase space is a dendrite even when we consider only the restriction on the set of periodic points.