Zero Entropy Is Generic

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چکیده

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Zero Entropy Is Generic

Dan Rudolph showed that for an amenable group, Γ, the generic measure-preserving action of Γ on a Lebesgue space has zero entropy. Here, this is extended to nonamenable groups. In fact, the proof shows that every action is a factor of a zero entropy action! This uses the strange phenomena that in the presence of nonamenability, entropy can increase under a factor map. The proof uses Seward’s re...

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ژورنال

عنوان ژورنال: Entropy

سال: 2016

ISSN: 1099-4300

DOI: 10.3390/e18060220