| Abstract: |
| In this talk, I will discuss recent joint work on entropies of intermediate factors.
For topological dynamical 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 $\varphi : Z \rightarrow Y$.
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 corollaries we also obtain results about the entropies of intermediate factors in the zero-dimensional setting.
Our proofs rely on a generalized Marker Lemma that holds for $G$-subshifts, where $G$ is any countable amenable group, which may be of independent interest. |
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