{"paper":{"title":"On the growth rate inequality for periodic points in the two sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Portela, A. Rovella, F. Valenzuela, G. Honorato, J. Iglesias, J. Xavier","submitted_at":"2017-07-19T15:14:51Z","abstract_excerpt":"Let $f:S^2\\to S^2$ be a continuous map such that $deg f = d, |d|>1$. Suppose $f$ has two attracting fixed points denoted $N$ and $S$ and let $A=S^2\\setminus \\{N,S\\}$. Assume that if a loop $\\gamma\\subset f^{-1}(A)$ is homotopically trivial in $A$, then $f(\\gamma)$ is also homotopically trivial in $A$. Then, for all $n$, $f$ has at least $|d^n -1|$ fixed points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06144","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"}