Relation between hyperbolic structure of partially hyperbolic systems and ergodic limit theorems

部分双曲系统的双曲结构与遍历极限定理之间的关系

• 批准号: 23740136
• 负责人: HATOMOTO Jin
• 金额: $ 0.17万
• 依托单位: Tokyo National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740136/
• 关键词: 部分双曲系; 弱双曲積構造; SRB 測度; 時間相関関数の多項式的減衰; SRB測度; オールモースト・アノソフ系; 双曲積構造; 相関関数の減衰; 中心極限定理(CLT); 大偏差原理(LDP)

We dealt with discrete time dynamical systems with weak hyperbolic product structure. We established polynomial upper bounds on large deviations for such dynamical systems associated with its Sinai-Ruelle-Bowen(SRB) measure if the return tail of the weak hyperbolic product structure decays polynomially. Applications of our results are some almost Anosov diffeomorphisms with uniformly contracting direction of which restriction on one dimensional center unstable direction behaves as a Manneville-Pomeau map.

研究了具有弱双曲乘积结构的离散时间动力系统。如果弱双曲乘积结构的返回尾多项式衰减，我们建立了与其Sinai-Ruelle-Bowen（SRB）测度相关的动力系统的大偏差的多项式上界.我们的结果应用于某些具有一致收缩方向的几乎Anosov同态，其一维中心不稳定方向的限制表现为Manneville-Pomeau映射。

项目成果

Polynomial upper bounds on large and moderate deviations for diffeomorphisms with weak hyperbolic product structure

具有弱双曲积结构的微分同胚的大偏差和中偏差的多项式上限

• 发表时间: 2012
• 期刊: Far East J Math Sci.
• 作者: 村瀬勇介;伊藤昭夫;Jin Hatomoto
• 通讯作者: Jin Hatomoto