On rotation sets for angular velocity

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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."