| Abstract: |
| We consider an arbitrary finite-to-one extension $X$ of a topological dynamical system $Y$ and count the number of ways to lift an invariant measure on the base system $Y$, up to multiplicity. In addition, we analyze the structure of arbitrary (possibly infinite-to-one) factor maps between symbolic dynamical systems and consider the problem of counting the number of ways to lift an invariant measure in an entropy maximizing way. This will involve the use of tools like class degree, relative equilibrium states, and Poulsen simplex. |
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