| Project/Area Number |
15H06416
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Shimane University |
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Principal Investigator |
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| Research Collaborator |
SUMI Hiroki 京都大学, 大学院人間・環境学研究科共生人間学専攻数理科学講座, 教授 (40313324)
MATSUZAKI Katsuhiko 早稲田大学, 教育・総合科学学術院, 教授 (80222298)
KESSEBÖHMER Marc University Bremen
STADLBAUER Manuel University of Rio de Janeiro
MUNDAY Sara University of Bologna
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| Project Period (FY) |
2015-08-28 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | Ergodic theory / Dynamical systems / Fractal Geometry / Hyperbolic Geometry / Geometric group theory / エルゴード理論 |
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| Outline of Final Research Achievements |
We have investigated the interplay of dynamics and geometry of conformal semigroup actions. Two of the main results are the following.
1) We have applied the multifractal analysis to random complex dynamical systems. In particular, we have investigated the Hoelder exponent of the long-term behavior depending on the initial value (J. Jaerisch, H. Sumi, Adv. Math 313 (2017), 36 pages).
2) We have investigated the Poincare exponent of abstract free groups and its normal subgroups. In the proof we use the discrete Laplacian on the associated Cayley graph (J. Jaerisch, K. Matsuzaki, Proc. AMS, to appear 2017).
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