1. We answer Michael Gordins 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 Roys theorem on
multiple mixing of Poisson suspensions, adding new examples to Jonathan Kings ergodic homoclinic groups of special zero-entropy transformations. 3. Sasha Prikhodko 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
We study the generalizations of Jonathan Kings rank-one theorems (Weak-Closure Theorem and rigidity of factors) to the case of rank-one R-actions (flows) and rank-one Z^n-actions. We prove that these results remain valid in the case of rank-one flows
. In the case of rank-one Z^n actions, where counterexamples have already been given, we prove partial Weak-Closure Theorem and partial rigidity of factors.
