{"paper":{"title":"Directional dimensions of ergodic currents on $\\mathbb C \\mathbb P (2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Axel Rogue, Christophe Dupont (IRMAR)","submitted_at":"2017-10-10T11:08:18Z","abstract_excerpt":"LLet $f$ be a holomorphic endomorphism of $\\mathbb P^ 2$ of degree $d \\geq 2$. We estimate the local directional dimensions of closed positive currents $S$ with respect to ergodic dilating measures $\\nu$.  We infer several applications. The first one shows that the currents $S$ containing a measure of entropy $h\\_\\nu > \\log d$ have a directional dimension $>2$, which answers a question by de Th\\'elin-Vigny. The second application asserts that the Dujardin's semi-extremal endomorphisms are close to suspensions of one-dimensional Latt\\`es maps. Finally, we obtain an upper bound for the dimension"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03508","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"}