Statistical properties of unimodal maps: the quadratic family

• 成果类型: Article
• 署名作者: Avila, A; Moreira, CG
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.161.831
• 发表日期: 2005
• 页码: 831-881
• 关键词: dynamics; POLYNOMIALS; HYPERBOLICITY; attractors; conjecture

摘要

We prove that almost every nonregular real quadratic map is Collet-Eckmann and has polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that typical quadratic maps have excellent ergodic properties, as exponential decay of correlations (Keller and Nowicki, Young) and stochastic stability in the strong sense (Baladi and Viana). This is an important step in achieving the same results for more general families of unimodal maps.