{"paper":{"title":"Fatou directions along the Julia set for endomorphisms of CP^k","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Romain Dujardin","submitted_at":"2010-06-04T12:46:48Z","abstract_excerpt":"Not much is known about the dynamics outside the support of the maximal entropy measure $\\mu$ for holomorphic endomorphisms of $\\mathbb{CP}^k$. In this article we study the structure of the dynamics on the Julia set, which is typically larger than $Supp(\\mu)$. The Julia set is the support of the so-called Green current $T$, so it admits a natural filtration by the supports of the exterior powers of $T$. For $1\\leq q \\leq k$, let $J_q= Supp(T^q)$. We show that for a generic point of $J_q\\setminus J_{q+1}$ there are at least $(k-q)$ \"Fatou directions\" in the tangent space. We also give estimates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0882","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"}