Inverses, powers and cartesian products of topologically deterministic maps

Michael Hochman, Artur Siemaszko

Abstract


We show that if $(X,T)$ is a topological dynamical system which is
deterministic in the sense of Kamiński, Siemaszko and Szymański
then $(X,T^{-1})$ and $(X\times X,T\times T)$ need not be deterministic
in this sense. However if $(X\times X,T\times T)$ is deterministic
then $(X,T^{n})$ is deterministic for all $n\in{\mathbb{N}}\setminus\{0\}$.

Keywords


Topological dynamics; topological determinism; recurrence

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