{"paper":{"title":"Mating quadratic maps with the modular group II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Luna Lomonaco, Shaun Bullett","submitted_at":"2016-11-16T12:37:32Z","abstract_excerpt":"In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of $(2:2)$ holomorphic correspondences $\\mathcal{F}_a$: $$\\left(\\frac{aw-1}{w-1}\\right)^2+\\left(\\frac{aw-1}{w-1}\\right)\\left(\\frac{az+1}{z+1}\\right) +\\left(\\frac{az+1}{z+1}\\right)^2=3$$ and proved that for every value of $a \\in [4,7] \\subset \\mathbb{R}$ the correspondence $\\mathcal{F}_a$ is a mating between a quadratic polynomial $Q_c(z)=z^2+c,\\,\\,c \\in \\mathbb{R}$ and the modular group $\\Gamma=PSL(2,\\mathbb{Z})$. They conjectured that this is the case for every member of the family $\\mathcal{F}_a$ which has $a$ in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05257","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"}