{"paper":{"title":"Rigidity Theorems for H\\'{e}non maps-II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Sayani Bera","submitted_at":"2019-02-25T15:33:15Z","abstract_excerpt":"The purpose of this note is to explore further the rigidity properties of H\\'{e}non maps from arXiv:1806.08189. For instance, we show that if $H$ and $F$ are H\\'{e}non maps with the same Green measure ($\\mu_H=\\mu_F$), or the same filled Julia set ($K_H=K_F$), or the same Green function ($G_H=G_F$), then $H^2$ and $F^2$ have to commute. This, in turn, gives that $H$ and $F$ have the same non-escaping sets. Further we prove that, either of the association of a H\\'{e}non map $H$ to its Green measure $\\mu_H$ or to its filled Julia set $K_H$ or to its Green function $G_H$ is locally injective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09369","kind":"arxiv","version":2},"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"}