| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Research Abstract |
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."
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