On rotation sets for angular velocity

本研究的目的是通过检查沿轨道的切向量的扭曲来找到周期轨道。我从速度和无穷小扭转的角度证明了周期轨道的存在性，并从拓扑的角度对连通极小集进行了分类。此外，我在最小集合中描述了沿轨道角度的变化。作为主要成果，我证明了以下定理（与松本茂典合著）；设f是一个具有非平凡连续统作为最小集的球的保向同胚。那么在最小集的补中就有两个不变的定义域而其他的定义域都在游荡"

The purpose of this study is to find periodic orbits by examining the twist of the tangent vectors along the orbits. I showed the existence of periodic orbits from the velocity and the infinitesimal twist, and also classified connected minimal sets from the topological points of view. Furthermore I characterized the variation of angles along the orbits in minimal sets. As a main result, I proved the following theorem (a joint work with Shigenori Matsumoto) ; "Let f be an orientation preserving homeomorphism of the sphere which has a nontrivial continuum as a minimal set. Then there are exactly two invariant domains in the complement of the minimal set and all the other domains are wandering."