Hereditary subshifts whose measure of maximal entropy has no Gibbs property

Fuente: arXiv
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Main Authors: Kułaga-Przymus, Joanna, Lemańczyk, Michał
Format: Preprint
Published: 2020
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author Kułaga-Przymus, Joanna
Lemańczyk, Michał
author_facet Kułaga-Przymus, Joanna
Lemańczyk, Michał
contents We show that the measure of maximal entropy for the hereditary closure of a $\mathscr{B}$-free subshift has the Gibbs property if and only if the Mirsky measure of the subshift is purely atomic. This answers an open question asked by Peckner. Moreover, we show that $\mathscr{B}$ is taut whenever the corresponding Mirsky measure $ν_η$ has full support. This is the converse theorem to a recent result of Keller.
format Preprint
id arxiv_https___arxiv_org_abs_2004_07643
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Hereditary subshifts whose measure of maximal entropy has no Gibbs property
Kułaga-Przymus, Joanna
Lemańczyk, Michał
Dynamical Systems
Probability
We show that the measure of maximal entropy for the hereditary closure of a $\mathscr{B}$-free subshift has the Gibbs property if and only if the Mirsky measure of the subshift is purely atomic. This answers an open question asked by Peckner. Moreover, we show that $\mathscr{B}$ is taut whenever the corresponding Mirsky measure $ν_η$ has full support. This is the converse theorem to a recent result of Keller.
title Hereditary subshifts whose measure of maximal entropy has no Gibbs property
topic Dynamical Systems
Probability
url https://arxiv.org/abs/2004.07643