{"paper":{"title":"On self-similarities of ergodic flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre I. Danilenko, Valery V. Ryzhikov","submitted_at":"2010-11-01T15:21:57Z","abstract_excerpt":"Given an ergodic flow $T=(T_t)_{t\\in\\Bbb R}$, let $I(T)$ be the set of reals $s\\ne 0$ for which the flows $(T_{st})_{t\\in\\Bbb R}$ and $T$ are isomorphic. It is proved that $I(T)$ is a Borel subset of $\\Bbb R^*$. It carries a natural Polish group topology which is stronger than the topology induced from $\\Bbb R$. There exists a mixing flow $T$ such that $I(T)$ is an uncountable meager subset of $\\Bbb R^*$. For a generic flow $T$, the transformations $T_{t_1}$ and $T_{t_2}$ are spectrally disjoint whenever $|t_1|\\ne |t_2|$. A generic transformation (i) embeds into a flow $T$ with $I(T)=\\{1\\}$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0343","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"}