Cantor subsystems on the Gehman dendrite.

Abstract

In the present paper, we focus on dynamical systems on the Gehman dendrite G. It is well-known that the set of end points of this dendrite is homeomorphic to the standard Cantor ternary set C. For any given surjective dynamical system acting on C, we provide constructions of dynamical systems on G, which are (i) topologically mixing but not exact or (ii) topologically exact, and such that in both cases, the subsystem acting on the set of end points End(G) is conjugate to the initially chosen dynamical system on C.