TY - JOUR
T1 - On invariant measures for B-free systems
AU - Kułaga-Przymus, Joanna
AU - Lemańczyk, Mariusz
AU - Weiss, Benjamin
N1 - Publisher Copyright:
© 2015 London Mathematical Society.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84942279798&partnerID=8YFLogxK
U2 - 10.1112/plms/pdv017
DO - 10.1112/plms/pdv017
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AN - SCOPUS:84942279798
SN - 0024-6115
VL - 110
SP - 1435
EP - 1474
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
IS - 6
ER -