{"paper":{"title":"On non-measurable sets and invariant tori","license":"","headline":"","cross_cats":["physics.gen-ph"],"primary_cat":"physics.class-ph","authors_text":"Krzysztof W. Wojciechowski, Piotr Pieranski","submitted_at":"2001-03-20T13:12:39Z","abstract_excerpt":"The question: \"How many different trajectories are there on a single invariant torus within the phase space of an integrable Hamiltonian system?\" is posed. A rigorous answer to the question is found both for the rational and the irrational tori. The relevant notion of non-measurable sets is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0103058","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"}