{"paper":{"title":"On the isomorphism of tensor powers of ergodic flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Valery V. Ryzhikov","submitted_at":"2016-10-31T19:51:53Z","abstract_excerpt":"The following question due to Thouvenot is well-known in ergodic theory. Let $S$ and $T$ be automorphisms of a probability space and let $ S \\otimes S $ be isomorphic to $T \\otimes T $. Could $S$ be not isomorphic to $T$? Our note contains a simple answer to this question and a generalization of Kulaga's result on the corresponding isomorphism for some class of flows (see arXiv:1101.4975). We show that the isomorphism of weakly mixing flows $ S_t \\otimes S_t $ and $ T_t \\otimes T_t $ implies the isomorphism of the flows $S_t$ and $T_t$, if the latter has an integral weak limit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.10093","kind":"arxiv","version":4},"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"}