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 |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Aoyama Gakuin University |
Principal Investigator |
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Project Period (FY) |
2011-04-28 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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Keywords | 位相幾何学 / 力学系理論 / 極小集合 / 位相幾何 / 力学系 / 幾何学 |
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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Report
(6 results)
Research Products
(9 results)