6 papers · 1 filter
Characteristic measures for language stable subshifts
Van Cyr, Bryna Kra
We consider the problem of when a symbolic dynamical system supports a Borel probability measure that is invariant under every element of its automorphism group. It follows readily…
The complexity threshold for the emergence of Kakutani inequivalence
Van Cyr, Aimee Johnson, Bryna Kra +1
We show that linear complexity is the threshold for the emergence of Kakutani inequivalence for measurable systems supported on a minimal subshift. In particular, we show that ther…
Boshernitzan's condition, factor complexity, and an application
Van Cyr, Bryna Kra
Boshernitzan found a decay condition on the measure of cylinder sets that implies unique ergodicity for minimal subshifts. Interest in the properties of subshifts satisfying this c…
Realizing ergodic properties in zero entropy subshifts
Van Cyr, Bryna Kra
A subshift with linear block complexity has at most countably many ergodic measures, and we continue of the study of the relation between such complexity and the invariant measures…
Free ergodic -systems and complexity
Van Cyr, Bryna Kra
Using results relating the complexity of a two dimensional subshift to its periodicity, we obtain an application to the well-known conjecture of Furstenberg on a Borel probability…
Counting generic measures for a subshift of linear growth
Van Cyr, Bryna Kra
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 assumpti…