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Topological slow entropy, sequence entropy, and generalized $[T,T^{-1}]$ systems
Nicanor Carrasco-Vargas
https://arxiv.org/abs/2506.17932 https://

Topological slow entropy, sequence entropy, and generalized $[T,T^{-1}]$ systems
We consider topological dynamical systems given by skew products $S\rtimes_τ T$, where $S\colon Y\to Y$ is a subshift, $τ\colon Y\to\mathbb{Z}$ is a continuous cocycle, and $T$ is an arbitrary invertible topological system. For fixed $(Y,S,τ)$ it may happen that all systems of the form $S\rtimes_τT$ have the same topological entropy, and thus it arises the problem of distinguishing two such systems. We show that if $T_1$ and $T_2$ are invertible topological dynamical systems with differen…