{"paper":{"title":"A condition that implies full homotopical complexity of orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bruno de Paula Jacoia, Salvador Addas-Zanata","submitted_at":"2018-04-11T04:13:38Z","abstract_excerpt":"We consider closed orientable surfaces $S$ of genus $g>1$ and homeomorphisms $f:S\\rightarrow S$ homotopic to the identity. A set of hypotheses is presented, called fully essential system of curves $\\mathscr{C}$ and it is shown that under these hypotheses, the natural lift of $f$ to the universal cover of $S$ (the Poincar\\'e disk $\\mathbb{D}),$ denoted $\\widetilde{f},$ has complicated and rich dynamics. In this context we generalize results that hold for homeomorphisms of the torus homotopic to the identity when their rotation sets contain zero in the interior. In particular, we prove that if $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04505","kind":"arxiv","version":3},"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"}