On rotation sets for angular velocity

本研究的目的是通过考察切向量沿着轨道的扭转来寻找周期轨道。从速度和无穷小扭曲度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，我的特点是变化的角度沿着轨道的极小集。作为一个主要的结果，我证明了以下定理（一个联合工作与Shigenori松本）;“设f是一个方向保持同胚的领域，其中有一个非平凡的连续作为一个最小集。则在极小集的补集中恰好有两个不变域，并且所有其他域都是游荡的。"

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."