Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions

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