Mathematical Sciences: Rotation and Entropy of Surface Homeomorphisms

本研究将集中在同胚理论上 表面，特别是旋转和拓扑熵。 的 该项目的核心是核查 环面或环面中本质同宿轨的存在性 同胚通过指定旋转行为是 足够复杂，在精确的意义上，由 映射的旋转熵。 该研究还将 试图制定一个正确的概念，旋转矢量上的一个 表面的高等属，作为一种手段，建立新的标准 对于存在的周期轨道的一个指定的旋转 复杂性 这项研究是在界面的表面拓扑结构， 动力系统 它利用了有趣的联系 各种拓扑和动力学概念之间的联系 维度系统

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.