Flexibility of statistical properties for smooth systems satisfying the central limit theorem

• 成果类型: Article
• 署名作者: Dolgopyat, Dmitry; Dong, Changguang; Kanigowski, Adam; Nandori, Peter
• 署名单位: University System of Maryland; University of Maryland College Park; Yeshiva University; Nankai University; Nankai University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01121-0
• 发表日期: 2022
• 页码: 31-120
• 关键词: planar lorentz process; DYNAMICAL-SYSTEMS; mixing properties; group extensions; bernoulli; FLOWS; entropy; z(d)-actions; ergodicity; dimension

摘要

We exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties: Zero entropy; Weak but not strong mixing; (Polynomial) mixing but not K; K but not Bernoulli and mixing at arbitrary fast polynomial rate. We also give an example of a system satisfying the CLT where the normalizing sequence is regularly varying with index 1. All these examples are C-infinity except for a zero entropy diffeomorphism satisfying the CLT which can be made C-r for an arbitrary finite r.