On invariant measures for B-free systems

Joanna Kułaga-Przymus, Mariusz Lemańczyk, Benjamin Weiss

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We show that the B-free subshift (S,XB) associated to a B-free system is intrinsically ergodic, that is, it has exactly one measure of maximal entropy. Moreover, we study invariant measures for such systems. It is proved that each ergodic invariant measure is of joining type, determined by a joining of the Mirsky measure of a B'-free subshift contained in (S,XB) and an ergodic invariant measure of the full shift on {0, 1}Z. Moreover, each ergodic joining type measure yields a measure-theoretic dynamical system with infinite rational part of the spectrum corresponding to the above Mirsky measure. Finally, we show that, in general, hereditary systems may not be intrinsically ergodic.

Original languageEnglish
Pages (from-to)1435-1474
Number of pages40
JournalProceedings of the London Mathematical Society
Volume110
Issue number6
DOIs
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 London Mathematical Society.

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