{"paper":{"title":"Polynomial Diffeomorphisms of C^2: VI. Connectivity of J","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Eric Bedford, John Smillie","submitted_at":"1996-12-18T19:02:44Z","abstract_excerpt":"Given a polynomial diffeomorphism f: C^2 -> C^2 there is a set $J_f\\subset{\\bf C}^2$ which we call the Julia set of f. The set $J_f\\subset C^2$ plays the role of the Julia set $J\\subset{\\bf C}$ for a polynomial map of C.  In the study of polynomial maps of C a great deal of attention has been paid to the connectivity of the Julia set.  The focus of this paper is to investigate the J-connected/J-disconnected dichotomy in the case of polynomial diffeomorphisms of C^2.\n  The Jacobian determinant of f is constant. We make the standing assumption that $|det\\ Df|\\le 1$ (this can always be achieved b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9612203","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"}