Dynamical simplices and Fra\"iss\'e theory
Dynamical Systems
2019-10-09 v2 Logic
Abstract
We simplify a criterion (due to Ibarluc\'ia and the author) which characterizes dynamical simplices, that is, sets of probability measures on a Cantor space for which there exists a minimal homeomorphism of whose set of invariant measures coincides with . 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.
Cite
@article{arxiv.1705.03648,
title = {Dynamical simplices and Fra\"iss\'e theory},
author = {Julien Melleray},
journal= {arXiv preprint arXiv:1705.03648},
year = {2019}
}