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good measures

Ergodic Theory and Dynamical Systems (1)

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1 results

A context in which finite or unique ergodicity is generic
Part of
- Ergodic theory
- Topological dynamics
ANDY Q. YINGST
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 10 / October 2021

Published online by Cambridge University Press:

29 September 2020, pp. 3178-3200

Print publication:

October 2021
- Article
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We show that for good measures, the set of homeomorphisms of Cantor space which preserve that measure and which have no invariant clopen sets contains a residual set of homeomorphisms which are uniquely ergodic. Additionally, we show that for refinable Bernoulli trial measures, the same set of homeomorphisms contains a residual set of homeomorphisms which admit only finitely many ergodic measures.