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Quasi-similarity and joining-stable invariants of ergodic actions

Valery V. RyzhikovJean-Paul Thouvenot
Mar 2023
摘要
Answering Vershik's question we show that quasi-similarity does not conservethe entropy, proving quasi-similarity of all Bernoulli actions of the groupswith an element of infinite order. We produce joining-stable invariantsconsidering zero $P$-entropy systems and prove an analog of Pinsker's theoremestablishing the disjointness of such systems with the actions of comletelypositive $P$-entropy. Then we apply Poisson suspensions to get a class of thecorresponding examples.
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