项目名称: 无穷维随机动力系统的SRB测度
项目编号: No.11301417
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 历智明
作者单位: 西北大学
项目金额: 23万元
中文摘要: 随机动力系统作为基础数学中随机分析与动力系统的交叉方向,特别是对系统复杂性与随机性之间关系的刻画一直是动力系统研究中的热点问题。 在光滑遍历论中,可微映射的所有不变测度里,Sinai-Ruell-Bowen(SRB)测度被认为是最有物理意义的,其存在性及相关性质的研究构成一个重要的课题。 本项目拟对无穷维随机系统的SRB测度展开研究。尝试研究双曲耦合系统(进而更一般的无穷维系统)的SRB测度的随机稳定性以及SRB测度关于系统在随机扰动下的可微性及其导数,即建立随机线性响应公式。从而刻画系统维数、随机扰动、双曲性和耦合结构对SRB测度的影响。
中文关键词: 熵;随机动力系统;双曲系统;平衡态;耦合格点
英文摘要: Random dynamical system as an interdisciplinary of stochastic analysis and dynamical system,especially describing the relation among complexity and rondomness in system is always an hot issue in the research of dynamical system. In smooth ergodic thoery, among all the inviriant measures of differentiable maps, Sinai-Ruelle-Bowen( SRB ) measures are considered to be most physical, and their existence and related propertise constitute one of the most significant topics of research. In this project, we attempt to do research on SRB measures in infinit dimentional random dynamical system. A linear respose formula of SRB measures with respect to random perturbations of hyperbolic coupled lattice( and other more general infinit dimensional systems ) will be established and the random stability of these SRB measures will be given . Furthermore, we will probe into the influences of dimensions, hyperbolicity, coupled structrue and random perturbations to the SRB measures.
英文关键词: entropy;random dynamical systems;hyperbolic systems;equilibrium state;coupled map lattices