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Dynamical simplices and Borel complexity of orbit equivalence

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Abstract

We prove that any divisible dynamical simplex is the set of invariant measures of some Toeplitz subshift. We apply our construction to prove that orbit equivalence of Toeplitz subshifts is Borel bireducible to the universal equivalence relation induced by a Borel action of S.

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Correspondence to Julien Melleray.

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Melleray, J. Dynamical simplices and Borel complexity of orbit equivalence. Isr. J. Math. (2020). https://doi.org/10.1007/s11856-020-1976-1

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