{"paper":{"title":"Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Valery Ryzhikov","submitted_at":"2014-04-01T19:40:58Z","abstract_excerpt":"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.\n  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.\n  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.\n  This version is based on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0361","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}