2015 Fiscal Year Final Research Report
Classification of connected exceptional minimal sets of 2-dimensional dynamical systems
| Project/Area Number |
23540104
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Aoyama Gakuin University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Keywords | 位相幾何学 / 力学系理論 |
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| Outline of Final Research Achievements |
The discrete dynamical system is a subject to examine the topological behavior of the orbits of homeomorphisms. We have many results on the dynamical study of the circle. In this study, we raised the dimension and studied diffeomorphisms of surfaces. As a result, we constructed a diffeomorphism of a surface with a connected minimal set which is not locally connected. Furthermore, we obtain some characterization of the dynamical behavior of diffeomorphisms of the surfaces. Among the compact invariant sets, the minimal sets in terms of the inclusion are called minimal sets. The orbits always wind around the minimal sets. In this sense, it is an important mathematical advance to find a new minimal set.
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| Free Research Field |
位相幾何学
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