拓扑动力系统中的多重传递及其相关问题

项目名称： 拓扑动力系统中的多重传递及其相关问题

项目编号： No.11471125

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： 吕杰

作者单位： 华南师范大学

项目金额： 45万元

中文摘要： 本项目主要研究拓扑动力系统中的多重传递性, 即研究由定义在紧致度量空间上的连续自映射的某些迭代的乘积映射的传递性及其相关问题. 我们已经借助于开集碰撞时间集和点的族传递的概念对多重传递性给出了等价刻画, 藉此,我们将探索从沿某序列的复杂性函数和弱不交性等其它角度给出多重传递属性进一步刻画, 揭示一个映射的某些迭代诱导的若干个乘积系统在传递性质方面的内在关联, 并且讨论多重传递属性与混沌等其它动力学性质的关系, 以期获得在传递系统的分类方面的相关结果, 并给出多重传递属性在组合数论等其它学科的应用.

中文关键词： 动力系统；多重传递性；Furstenberg族；制约关系；混沌

英文摘要： This project is devoted to research multi-transitivity in topological dynamcail system, in other wrods, we focus on the transitivity of the product map induced by some iterations of a continuous map from compact metric space onto itself. Base on the result we obtained that give an equivalent statement of multi-transitivity via hitting time set of two open subsets in state space, we will explore other characterizations of multi-transitivity of dynamical system via its complexity functions along sequences or weak disjointness, reveal the implications concerning transitivity among a family of product systems, and establish the connections between multi-transitivity and other dynamical properties, such as chaos in some sense. We hope the research should help to refine classification of transitive systems and can be applied to some science fields, such as combinatorial number theory.

英文关键词： dynamics;multi-transitivity;Furstenberg family;implication;chaos