{"paper":{"title":"Robust entropy expansiveness implies generic domination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J. L. Vieitez, M. J. Pacifico","submitted_at":"2009-03-17T11:57:57Z","abstract_excerpt":"Let $f: M \\to M$ be a $C^r$-diffeomorphism, $r\\geq 1$, defined on a compact boundaryless $d$-dimensional manifold $M$, $d\\geq 2$, and let $H(p)$ be the homoclinic class associated to the hyperbolic periodic point $p$. We prove that if there exists a $C^1$ neighborhood $\\mathcal{U}$ of $f$ such that for every $g\\in {\\mathcal U}$ the continuation $H(p_g)$ of $H(p)$ is entropy-expansive then there is a $Df$-invariant dominated splitting for $H(p)$ of the form $E\\oplus F_1\\oplus... \\oplus F_c\\oplus G$ where $E$ is contracting, $G$ is expanding and all $F_j$ are one dimensional and not hyperbolic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2948","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"}