A proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type

• 成果类型: Article
• 署名作者: Cheraghi, Davoud; Cheritat, Arnaud
• 署名单位: Imperial College London; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0576-2
• 发表日期: 2015
• 页码: 677-742
• 关键词: quadratic siegel disks; brjuno functions; julia sets; size

摘要

Marmi, Moussa and Yoccoz conjectured that some error function , related to the approximation of the size of Siegel disks by some arithmetic function of the rotation number , is a Holder continuous function of with exponent . Using the renormalization invariant class of Inou and Shishikura, we prove this conjecture for the restriction of to a class of high type numbers.