{"paper":{"title":"Correspondences in complex dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Siqueira, Luna Lomonaco, Shaun Bullett","submitted_at":"2017-10-10T03:06:34Z","abstract_excerpt":"This paper surveys some recent results concerning the dynamics of two families of holomorphic correspondences, namely ${\\mathcal F}_a:z \\to w$ defined by the relation $$\\left( \\frac{aw-1}{w-1} \\right)^2 + \\left( \\frac{aw-1}{w-1} \\right) \\left( \\frac{az +1}{z+1} \\right) + \\left( \\frac{az+1}{z+1} \\right)^2 =3,$$ and $$\\mathbf{f}_c(z)=z^{\\beta} +c, \\mbox{ where } 1<\\beta=p/q \\in \\mathbb{Q},$$ which is the correspondence $\\mathbf{f}_c:z \\to w$ defined by the relation $$(w-c)^q=z^p.$$ Both can be regarded as generalizations of the family of quadratic maps $f_c(z)=z^2+c$. We describe dynamical prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03385","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"}