Counting generic measures for a subshift of linear growth

Van Cyr, Bryna Kra

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In 1984 Boshernitzan proved an upper bound on the number of ergodic measures for a minimal subshift of linear block growth and asked if it could be lowered without further assumptions on the shift. We answer this question, showing that Boshernitzan’s bound is sharp. We further prove that the same bound holds for the, a priori, larger set of nonatomic generic measures, and that this bound remains valid even if one drops the assumption of minimality. Applying these results to interval exchange transformations, we give an upper bound on the number of nonatomic generic measures of a minimal IET, answering a question recently posed by Chaika and Masur.

Original languageEnglish (US)
Pages (from-to)355-380
Number of pages26
JournalJournal of the European Mathematical Society
Issue number2
StatePublished - 2019


  • Automorphism
  • Block complexity
  • Interval exchange transformation
  • Subshift

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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