Solenoidal attractors with bounded combinatorics are shy

• 成果类型: Article
• 署名作者: Smania, Daniel
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.191.1.1
• 发表日期: 2020
• 页码: 1-79
• 关键词: universal metric properties; invariant splittings; Stochastic dynamics; HYPERBOLICITY; MAPS; RENORMALIZATION; EXISTENCE; families; dichotomies; RIGIDITY

摘要

We show that in a generic finite-dimensional real-analytic family of real-analytic multimodal maps, the subset of parameters on which the corresponding map has a solenoidal attractor with bounded combinatorics is a set with zero Lebesgue measure.