{"paper":{"title":"On the support of measures of large entropy for H\\'enon-Sibony maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Sobir Boymurodov","submitted_at":"2026-06-07T17:54:36Z","abstract_excerpt":"Let $f$ be a H\\'enon-Sibony map of $\\mathbb{C}^k$ of algebraic degree $d_+\\geq 2$, whose inverse $f^{-1}$ has algebraic degree $d_-$. The topological entropy of $f$ is equal to $\\log d_+^{p} = \\log d_-^{k-p}$. We show that every ergodic $f$-invariant measure $\\nu$ satisfying $h_\\nu(f)>\\log \\max\\{ d_+^{p-1},d_-^{k-p-1}\\}$ is supported on the Julia set $\\mathcal{J}$ of $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08754","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08754/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}