{"paper":{"title":"Limit directions of a vector cocycle, remarks and examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Jean-Pierre Conze (IRMAR), St\\'ephane Le Borgne (IRMAR)","submitted_at":"2014-05-07T19:08:01Z","abstract_excerpt":"We study the set ${\\cal D}(\\Phi)$ of limit directions of a vector cocycle $(\\Phi_n)$ over a dynamical system, i.e., the set of limit values of $\\Phi_n(x) /\\|\\Phi_n(x)\\|$ along subsequences such that $\\|\\Phi_n(x)\\|$ tends to $\\infty$. This notion is natural in geometrical models of dynamical systems where the phase space is fibred over a basis with fibers isomorphic to $\\mathbb{R}^d$, like systems associated to the billiard in the plane with periodic obstacles. It has a meaning for transient or recurrent cocycles. Our aim is to present some results in a general context as well as for specific m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1989","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"}