Exponential decay of correlations for finite horizon Sinai billiard flows

• 成果类型: Article
• 署名作者: Baladi, Viviane; Demers, Mark F.; Liverani, Carlangelo
• 署名单位: Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Fairfield University; University of Rome Tor Vergata
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0745-1
• 发表日期: 2018
• 页码: 39-177
• 关键词: statistical properties; banach-spaces; systems

摘要

We prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L-t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions.