1998 Fiscal Year Final Research Report Summary
Deformation theory of Kleinian groups
| Project/Area Number |
09640162
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | Ochanomizu University |
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Principal Investigator |
WATANABE Hisako Ochanomizu University, Faculty of Science, Professor, 理学部, 教授 (70017193)
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| Co-Investigator(Kenkyū-buntansha) |
MAEDA Michie Ochanomizu University, Faculty of Science, Professor, 理学部, 教授 (30017206)
TANIZAKI Masahiko Kyoto University, Research Course in Science, Assistant Professor, 大学院・理学研究科, 助教授 (50108974)
MATSUZAKI Katsuhiko Ochanomizu University, Faculty of Science, Assistant Professor, 理学部, 助教授 (80222298)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Kleinian group / Fuchsian group / Hausdorff dimension / Teichmuller space / quasiconformal map / deformation / fractal set / dynamical system |
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| Research Abstract |
1. By geometric properties of corresponding a hyperbolic manifold we described the necessary conditions in order that the Hausdorff dimension of the limite of a n-dimensinal hyperbolic discrete group is less than n.
2. We investigated the continuity of the Hausdorff dimensions as the Kleinian groups are deformed.
3. We analized the structures of the set of discrete representations in the parameter space and proposed the method of analizing the structure of the space of quasi-Fuchsian groups by a holonomy map from the space of projections on a Riemann manifold.
4. We obtained the results on the structural stability of Kleinian groups under small perturbations and on the equivalence between the algebraic topology and the Teichm_ller one in the space of quasiconformal deformations.
5. We built the deformation theory of dynamical systems for entire functions on a ground of Teichm_ller space and found the fundamental properties of wan-dering domains and Baker domains, which rational functions don't have.
6. We investigated a family of inlaid functions and showed the topological completeness of it. Further we found the Teichm_ller spaces of the Fatou components of those functions.
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