2016 Fiscal Year Final Research Report
Rigidity problem on group actions with an invariant geometric structure
Project/Area Number |
26400085
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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 | Kyoto University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2017-03-31
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Keywords | 群作用 / 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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Free Research Field |
力学系
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