{"paper":{"title":"On hyperbolic metric and asymptotically finite invariant differentials in holomorphic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Cabrera, Peter Makienko","submitted_at":"2015-09-23T19:34:07Z","abstract_excerpt":"Given a rational map $R$, we consider the complement of the postcritical set $S_R$. In this paper we discuss the existence of invariant Beltrami differentials supported on a $R$ invariant subset $A$ of $S_R$. Under some geometrical restrictions, either on the hyperbolic geometry of $A$ or on the asymptotic behavior of infinitesimal geodesics of the Teichm\\\"uller space of $S_R$, we show the absence of invariant Beltrami differentials supported on $A$. In particular, we show that if $A$ has finite hyperbolic area, then $A$ can not support invariant Beltrami differentials except in the case where"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07105","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"}