{"paper":{"title":"The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions (Without Exceptional Models)","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Nandor Simanyi","submitted_at":"2004-07-22T03:27:47Z","abstract_excerpt":"We consider the system of $N$ ($\\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ in the flat unit torus $\\Bbb T^\\nu$, $\\nu\\ge2$. In the case $\\nu=2$ we prove (the full hyperbolicity and) the ergodicity of such systems for every selection $(m_1,...,m_N;r)$ of the external geometric parameters, without exceptional values. In higher dimensions, for hard ball systems in $\\Bbb T^\\nu$ ($\\nu\\ge3$), we prove that every such system (is fully hyperbolic and) has open ergodic components."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407368","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"}