Mathematical Sciences: Combinatorial Dynamics

数学科学：组合动力学

• 批准号: 9305899
• 负责人: Michal Misiurewicz
• 金额: $ 6.69万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305899&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatorial; Dynamics

Misiurewicz will investigate the conjecture that the only primary cycles for disk homeomorphisms are those with entropy zero. He will also look for pseudo-Anosov cycles of a given period with minimal entropy. A third problem will be to investigate the pseudo-Anosov cycles of torus homeomorphisms isotopic to the identity and try to analyze their rotation set. Combinatorial dynamics is a part of the theory of dynamical systems dealing mainly with existence of periodic orbits, or cycles, for various types of discrete dynamical systems. By a type of a cycle one understands in the simplest case of interval maps the way the map permutes its points. Very often existence of a cycle of a given type forces the existence of many other types of cycles for the same map. This model situation admits numerous generalizations.

Misiurewicz将调查以下猜想：磁盘同构的唯一主要循环是熵零的循环。 他还将寻找给定时期的伪anosov周期，其熵最少。 第三个问题将是研究同位素同位素的伪anosov循环，并尝试分析其旋转集。 组合动力学是针对各种离散动力学系统的周期性轨道或周期存在的动力系统理论的一部分。 通过一种类型的循环，一个人在最简单的情况下理解地图绘制其点的方式。 通常，给定类型的循环的存在迫使同一地图的许多其他类型的周期存在。 这种模型情况承认了许多概括。