{"paper":{"title":"On the self-similarity problem for Gaussian-Kronecker flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joanna Kulaga, Krzysztof Fraczek, Mariusz Lemanczyk","submitted_at":"2012-01-27T09:53:21Z","abstract_excerpt":"It is shown that a countable symmetric multiplicative subgroup $G=-H\\cup H$ with $H\\subset\\mathbb{R}_+^\\ast$ is the group of self-similarities of a Gaussian-Kronecker flow if and only if $H$ is additively $\\mathbb{Q}$-independent. In particular, a real number $s\\neq\\pm1$ is a scale of self-similarity of a Gaussian-Kronecker flow if and only if $s$ is transcendental. We also show that each countable symmetric subgroup of $\\mathbb{R}^\\ast$ can be realized as the group of self-similarities of a simple spectrum Gaussian flow having the Foias-Stratila property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5733","kind":"arxiv","version":2},"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"}