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Mixing properties of nearly maximal entropy measures for ℤ d shifts of finite type

E. Robinson, Ayşe Şahin (2000)

Colloquium Mathematicae

We prove that for a certain class of ℤ d shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.

On the countable generator theorem

Michael Keane, Jacek Serafin (1998)

Fundamenta Mathematicae

Let T be a finite entropy, aperiodic automorphism of a nonatomic probability space. We give an elementary proof of the existence of a finite entropy, countable generating partition for T.

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