Abstract
We characterize the class of functions which occur as the entropy function defined on the set of invariant measures of a (minimal) topological dynamical system. Namely, these are all non-negative affine functionsh, defined on metrizable Choquet simplices, which are non-decreasing limits of upper semi-continuous functions. Ifh is itself upper semi-continuous then it can be realized as the entropy function in an expansive dynamical system. The constructions are done effectively using minimal almost 1-1 extensions over a rotation of a group ofp-adic integers (in the expansive case, the construction leads to Toeplitz flows).
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