Rigidity problem on group actions with an invariant geometric structure
Project/Area Number |
26400085
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Kyoto University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 群作用 / 力学系 / 周期軌道 / 群作用の剛性 / 野生的力学系 |
Outline of Final Research Achievements |
We obtained a local rigidity result for certain group action related to the rank-1 Lie group SO(n,1) with n>1 and a description of deformation of certain group action on the torus which preserves a geometric structure. The latter was an application of a method to show a rigidity result for a conformal action on the sphere. We also proved the abundance of super-exponential growth of the number of periodic points and existence of universal dynamics for one-dimensional iterated function systems which satisfies some mild conditions. One-dimensional iterated function systems are toy models of partially hyperbolic dynamical systems. Hence, our result is a step to understand wild behavior of partially hyperbolic systems.
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Report
(4 results)
Research Products
(7 results)