Ubiquity of entropies of intermediate factors
| Autor: | McGoff, Kevin, Pavlov, Ronnie |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/jlms.12450 |
| Popis: | We consider topological dynamical systems $(X,T)$, where $X$ is a compact metrizable space and $T$ denotes an action of a countable amenable group $G$ on $X$ by homeomorphisms. For two such systems $(X,T)$ and $(Y,S)$ and a factor map $\pi : X \rightarrow Y$, an intermediate factor is a topological dynamical system $(Z,R)$ for which $\pi$ can be written as a composition of factor maps $\psi : X \rightarrow Z$ and $\varphi : Z \rightarrow Y$. In this paper we show that for any countable amenable group $G$, for any $G$-subshifts $(X,T)$ and $(Y,S)$, and for any factor map $ \pi :X \rightarrow Y$, the set of entropies of intermediate subshift factors is dense in the interval $[h(Y,S), h(X,T)]$. As a corollary, we also prove that if $(X,T)$ and $(Y,S)$ are zero-dimensional $G$-systems, then the set of entropies of intermediate zero-dimensional factors is equal to the interval $[h(Y,S), h(X,T)]$. Our proofs rely on a generalized Marker Lemma that may be of independent interest. Comment: The zero-dimensional results have been generalized and unified relative to the previous version |
| Databáze: | arXiv |
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