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Hereditary subshifts whose measure of maximal entropy does not have the Gibbs property

Volume 166 / 2021

Joanna Kułaga-Przymus, Michał D. Lemańczyk Colloquium Mathematicum 166 (2021), 107-127 MSC: Primary 37B10; Secondary 28D20. DOI: 10.4064/cm8223-11-2020 Published online: 2 March 2021


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.


  • Joanna Kułaga-PrzymusFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University in Toruń
    Chopina 12/18
    87-100 Toruń, Poland
  • Michał D. LemańczykFaculty of Mathematics, Informatics,
    and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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