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

Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions