{"paper":{"title":"Minimal geodesic foliation on T^2 in case of vanishing topological entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Eva Glasmachers, Gerhard Knieper","submitted_at":"2011-01-09T18:48:59Z","abstract_excerpt":"On a Riemannian 2-torus $(T^2,g)$ we study the geodesic flow in the case of low complexity described by zero topological entropy. We show that this assumption implies a nearly integrable behavior. In our previous paper \\cite{GK} we already obtained that the asymptotic direction and therefore also the rotation number exists for all geodesics. In this paper we show that for all $r \\in \\mathbb{R} \\cup \\{\\infty\\}$ the universal cover $\\Br^2$ is foliated by minimal geodesics of rotation number $r$. For irrational $r \\in \\mathbb{R}$ all geodesics are minimal, for rational $r \\in \\mathbb{R} \\cup \\{\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1660","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"}