Abstract |
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. In this talk I
will discuss recent work (joint with B. Kra) in which we show that
Boshernitzan's bound is sharp. Our methods allow us to study the, a priori,
larger set of nonatomic generic measures, and one of our main results gives
a bound on the size of this set for a minimal Interval Exchange
Transformation.
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