Mathematical Sciences: Rotation and Entropy of Surface Homeomorphisms

数学科学：表面同态的旋转和熵

• 批准号: 9007553
• 负责人: Richard Swanson
• 金额: $ 2.06万
• 依托单位: Montana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007553&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Rotation; Entropy; Surface

This research will focus on the theory of homeomorphisms on surfaces, specifically rotation and topological entropy. The core of the project deals with the problem of verifying the existence of essential homoclinic orbits in annulus or toral homeomorphisms by specifying that the rotational behavior be sufficiently complex, in a precise sense, as measured by the rotational entropy of the mapping. The research will also attempt to formulate a correct notion of a rotational vector on a surface of higher genus, as a means of establishing new criteria for the existence of periodic orbits of a specified rotational complexity. This research is at the interface of surface topology and dynamical systems. It makes use of interesting connections between various topological and dynamical notions in low dimensional systems.

本研究将集中于曲面上的同胚理论，特别是旋转和拓扑熵。该项目的核心是通过指定旋转行为足够复杂，在精确意义上，通过映射的旋转熵来测量，来验证环空或全同胚中基本同斜轨道的存在性问题。本研究还将尝试在高属曲面上建立一个正确的旋转矢量概念，作为建立具有特定旋转复杂度的周期轨道存在性的新准则的一种手段。本研究是表面拓扑学和动力系统的结合。它利用了低维系统中各种拓扑和动力学概念之间的有趣联系。