Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions
Dynamical Systems
2014-04-02 v1
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
Cite
@article{arxiv.1404.0361,
title = {Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions},
author = {Valery Ryzhikov},
journal= {arXiv preprint arXiv:1404.0361},
year = {2014}
}
Comments
in Russian, ergodic theory