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arXiv · 1404.0361

Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions

Valery Ryzhikov
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Abstract

1. We answer Michael Gordin's question providing singular spectrum for transformations with homoclinic Bernoulli flows via Poisson suspensions induced by modified Sidon rank-one constructions. 2. We give homoclinic proof of Emmanuel Roy's theorem on multiple mixing of Poisson suspensions, adding new examples to Jonathan King's ergodic homoclinic groups of special zero-entropy transformations. 3. Sasha Prikhod'ko found the fast decay of correlations for some iceberg automorphisms. We get similar correlations for a class of infinite rank-one Sidon transformations. This version is based on "On Mixing Rank One Infinite Transformations" arXiv:1106.4655

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Valery Ryzhikov. 2014-04-01. Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions. https://arxiv.org/abs/1404.0361

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