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arXiv · 1705.03648

Dynamical simplices and Fra\"iss\'e theory

Julien Melleray
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Abstract

We simplify a criterion (due to Ibarluc\'ia and the author) which characterizes dynamical simplices, that is, sets $K$ of probability measures on a Cantor space $X$ for which there exists a minimal homeomorphism of $X$ whose set of invariant measures coincides with $K$. We then point out that this criterion is related to Fra\"iss\'e theory, and use that connection to provide a new proof of Downarowicz' theorem stating that any Choquet simplex is affinely homeomorphic to a dynamical simplex. The construction enables us to prove that there exist minimal homeomorphisms of a Cantor space which are speedup equivalent but not orbit equivalent, answering a question of D. Ash.

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Julien Melleray. 2017-05-10. Dynamical simplices and Fra\"iss\'e theory. https://doi.org/10.1017/etds.2018.8

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