Hereditary subshifts whose measure of maximal entropy does not have the Gibbs property
Volume 166 / 2021
Colloquium Mathematicum 166 (2021), 107-127
MSC: Primary 37B10; Secondary 28D20.
DOI: 10.4064/cm8223-11-2020
Published online: 2 March 2021
Abstract
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 $\nu _\eta $ has full support. This is the converse to a recent result of Keller.
