Kupka-Smale theorem for polynomial automorphisms of C2 and persistence of heteroclinic intersections

• 成果类型: Article
• 署名作者: Buzzard, GT; Hruska, SL; Ilyashenko, Y
• 署名单位: Purdue University System; Purdue University; Cornell University; Lomonosov Moscow State University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0418-8
• 发表日期: 2005
• 页码: 45-89
• 关键词: holomorphic maps; PREVALENCE

摘要

A map is Kupka-Smale if all periodic points are hyperbolic and the stable and unstable manifolds of any two saddle points are transverse. Here we prove that Kupka-Smale maps form a residual set of full Lebesgue measure in the space P-d of polynomial automorphisms of C-2 of fixed dynamical degree d >= 2. We also prove that a heteroclinic point of two saddle periodic orbits may be continued over (almost) the entire parameter space for this set of maps. This is one of the first persistence theorems proved in holomorphic dynamics in several variables.