{"paper":{"title":"The symplectic structure of renormalisation of circle diffeomorphisms with breaks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"Konstantin Khanin, Selim Ghazouani","submitted_at":"2019-07-16T14:12:30Z","abstract_excerpt":"In this article we prove that iterated renormalisations of $\\mathcal{C}^r$ circle diffeomorphisms with $d$ breaks, $r>2$, with given size of breaks, converge to an invariant family of piecewise Moebius maps, of dimension $2d$. We prove that this invariant family identifies with a \\textit{relative character variety} $\\chi(\\pi_1 \\Sigma, \\mathrm{PSL}(2,\\mathbb{R}), \\mathbf{h})$ where $\\Sigma$ is a $d$-holed torus, and that the renormalisation operator identifies with a sub-action of the mapping class group $\\mathrm{MCG}(\\Sigma)$. This action is known to preserves a symplectic form, thanks to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07021","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"}