2001 Fiscal Year Final Research Report Summary
Research for higher dimensional Takagi functions
| Project/Area Number |
12640085
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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 |
Geometry
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| Research Institution | Aoyamagakuin University |
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Principal Investigator |
YANO Koichi Aoyamagakuin University, Faculty of Science and Engineering, Professor (60114691)
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| Co-Investigator(Kenkyū-buntansha) |
KOIKE Kazuhiko Aoyamagakuin University, Faculty of Science and Engineering, Professor (70146306)
NAKANE Takashi Aoyamagakuin University, Faculty of Science and Engineering, Associated Professor (50082805)
IHARA Shinichirou Aoyamagakuin University, Faculty of Science and Engineering, Professor (30012347)
YAMAGUCHI Manabu Aoyamagakuin University, Faculty of Science and Engineering, Assistant Professor (60306503)
TANIGUCHI Kenji Aoyamagakuin University, Faculty of Science and Engineering, Associated Professor (20306492)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Lyapunov index / dynamical systems / Takagi function |
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| Research Abstract |
Takagi function is an example of everywhere non-differentiable one variable functions due to Teiji Takagi, and is defined by a series using interval dynamical systems. Hattori defined a family of Takagi functions defined on a triangle, using a dynamical system naturally induced from barycentric subdivision of a triangle, and studied a relationship between the value of the parameter and the property of the function. One aim of this research was to study the property of original Takagi functions in case of the dynamics came from non-symmetric tent maps. But numerical computation about Lyapunov index of such Takagi functions and theoretical research do not develop new results. Another aim was to investigate three dimensional family of Takagi functions. But also numerical computation about Lyapunov index for this case and theoretical research using random matrix theory do not develop new results. On the hands, research for relevant topics, in particular about representation theory, we get results about spin representations and centralizer algebras, duality of a twisted group algebra of the hyperoctahedral group and the queer Lie superalgebra, Bernstein degree and associated cycles of Harish-Chandra modules.
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