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.

米西乌维奇将研究盘同胚的唯一主循环是熵为零的猜想。 他还将寻找给定时期的具有最小熵的伪阿诺索夫循环。 第三个问题是研究圆环同构同位素的伪阿诺索夫循环，并尝试分析它们的旋转集。 组合动力学是动力系统理论的一部分，主要研究各种类型的离散动力系统的周期轨道或循环的存在。 通过一种循环，我们可以理解在最简单的区间映射情况下映射排列其点的方式。 通常，给定类型的循环的存在会迫使同一地图存在许多其他类型的循环。 这种模型情况可以进行多种概括。