Limit theorems for fast-slow partially hyperbolic systems

• 成果类型: Article
• 署名作者: De Simoi, Jacopo; Liverani, Carlangelo
• 署名单位: University of Toronto; University of Rome Tor Vergata
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0798-9
• 发表日期: 2018
• 页码: 811-1016
• 关键词: statistical properties; transfer operators; DYNAMICAL-SYSTEMS; decay; spectrum; SPACES; FLOWS; MAPS

摘要

We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and conclude with a completely new result (a local limit theorem) on the distribution of the process determined by the fluctuations around the average. The method of proof is based on a mixture of standard pairs and transfer operators that we expect to be applicable in a much wider generality.