{"paper":{"title":"Diffeomorphisms with stable manifolds as basin boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Wolf, Sandra Hayes","submitted_at":"2013-10-15T12:32:48Z","abstract_excerpt":"In this paper we study the dynamics of a family of diffeomorphisms in $\\bR^2$ defined by $\nF(x,y)=(g(x)+h(y),h(x)), $\nwhere $ g(x) $ is a unimodal $C^2$-map which has the same dynamical properties as the logistic map $P(x)=\\mu x(1-x)$, and $h(x) $ is a $C^2$ map which is a small perturbation of a linear map. For certain maps of this form we show that there are exactly two periodic points, namely an attracting fixed point and a saddle fixed point and the boundary of the basin of attraction is the stable manifold of the saddle.\n  The basin boundary also has the same regularity as $F$, in contras"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4032","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"}