随机动力系统中熵结构与热力学形式的研究

项目名称： 随机动力系统中熵结构与热力学形式的研究

项目编号： No.11471114

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 马先锋

作者单位： 华东理工大学

项目金额： 68万元

中文摘要： 随机动力系统的热力学形式理论是随机动力系统中维数理论和重分形分析研究中的重要内容。在确定性动力系统中建立的熵结构理论是确定性动力系统热力学形式研究的重要工具。随机动力系统中热力学形式的发展为随机动力系统熵结构理论的建立提出了要求。本项目是随机动力系统的熵结构与热力学形式理论的结合性研究。运用随机动力系统中建立的熵结构理论研究随机热力学形式，并注重其在随机动力系统的维数理论，如随机非紧拓扑压的Bowen方程和重分形分析等问题研究中的应用。本项目的研究有助于加深人们对随机动力系统动力学性态的复杂性和几何结构的复杂性认识。

中文关键词： 随机动力系统；熵结构；热力学形式；遍历理论；重分形分析

英文摘要： The thermodynamic formalism for random dynamical systems is the crucial content in the research of dimension theory and multifractal analysis in random dynamical systems. The theory of entropy structures established in the deterministic dynamical systems has been a key tool in the field of the thermodynamic formalism. Requirements are proposed for the theory of entropy structures as the development of the thermodynamic formalism in random dynamical systems. This project is the combined study of the entropy structures and the thermodynamic formalism in random environment. We will conduct the research on the theory of the thermodynamic formalism through the constructed entropy structures in random dynamical systems. The applications of the thermodynamic formalism in the field of random fractals, such as the Bowen formula of the noncompact random topological pressures, multifractal analysis, etc., will also be considered. This research will be helpful for people further understanding the complexities of dynamical behaviors and geometric structures of random dynamical systems.

英文关键词： Random dynamical systems;Entropy structures;Thermodynamic formalism;Ergodic theory;Multifractal formalism