{"paper":{"title":"Flows with uncountable but meager group of self-similarities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre I. Danilenko","submitted_at":"2011-08-11T19:34:24Z","abstract_excerpt":"Given an ergodic probability preserving flow $T=(T_t)_{t\\in\\Bbb R}$, let $I(T):=\\{s\\in\\Bbb R^*\\mid T\\text{is isomorphic to}(T_{st})_{t\\in\\Bbb R}\\}$. A weakly mixing Gaussian flow $T$ is constructed such that $I(T)$ is uncountable and meager. For a Poisson flow $T$, a subgroup $I_{\\text{Po}}(T)\\subset I(T)$ of Poissonian self-similarities is introduced. Given a probability measure $\\kappa$ on $\\Bbb R^*_+$, a zero-entropy Poisson flow $T$ is constructed such that $I_{\\text{Po}}(T)$ is the group of $\\kappa$-quasi-invariance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2496","kind":"arxiv","version":3},"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"}