{"paper":{"title":"Coexistence of invariant sets with and without SRB measures in H\\'enon family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"math.DS","authors_text":"Ming-Chia Li, Shin Kiriki, Teruhiko Soma","submitted_at":"2010-07-09T02:49:51Z","abstract_excerpt":"Let $\\{f_{a,b}\\}$ be the (original) H\\'enon family. In this paper, we show that, for any $b$ near $0$, there exists a closed interval $J_b$ which contains a dense subset $J'$ such that, for any $a\\in J'$, $f_{a,b}$ has a quadratic homoclinic tangency associated with a saddle fixed point of $f_{a,b}$ which unfolds generically with respect to the one-parameter family $\\{f_{a,b}\\}_{a\\in J_b}$. By applying this result, we prove that $J_b$ contains a residual subset $A_b^{(2)}$ such that, for any $a\\in A_b^{(2)}$, $f_{a,b}$ admits the Newhouse phenomenon. Moreover, the interval $J_b$ contains a den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1500","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"}