{"paper":{"title":"Mating quadratic maps with the modular group III: The modular Mandelbrot set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Luna Lomonaco, Shaun Bullett","submitted_at":"2020-10-08T21:45:07Z","abstract_excerpt":"We prove that there exists a homeomorphism $\\chi$ between the connectedness locus $\\mathcal{M}_{\\Gamma}$ for the family $\\mathcal{F}_a$ of $(2:2)$ holomorphic correspondences introduced by Bullett and Penrose, and the parabolic Mandelbrot set $\\mathcal{M}_1$. The homeomorphism $\\chi$ is dynamical ($\\mathcal{F}_a$ is a mating between $PSL(2,\\mathbb{Z})$ and $P_{\\chi(a)}$), it is conformal on the interior of $\\mathcal{M}_{\\Gamma}$, and it extends to a homeomorphism between suitably defined neighbourhoods in the respective one parameter moduli spaces.\n  Following the recent proof by Petersen and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.04273","kind":"arxiv","version":5},"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/2010.04273/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"}