| Presentation | 1998/3/12 One dimensional dynamical system and Fractal Makoto Mori, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | To study ergodic properties of dynamical system, the corresponding Perron-Frobenius operator is one of the main tool.However, it is not compact, so we can not apply general spectral theories of operators.So we represent a dynamical system into a symbolic dynamics, and construct a renewal equation.Then we can define the Fredholm determinant which makes us possible to determine the spectra of the Perron-Frobenius operator concretely.This Fredholm determinant relates deeply to dynamical zeta function.We apply these theory to Cantor sets generated by piecewise linear maps.We not only study the Hausdorff dimension of the Cantor set, but also construct the invariant probability measure which is absolutely continuous to the Hausdorff measure and study its ergodicity. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | ergodicity / Perron-Frobenius operator / renewal equation / Fredholm determinant / zeta function / Cantor set |
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| Conference Information | |
| Committee | NLP |
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| Conference Date | 1998/3/12(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Nonlinear Problems (NLP) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | One dimensional dynamical system and Fractal |
| Sub Title (in English) | |
| Keyword(1) | ergodicity |
| Keyword(2) | Perron-Frobenius operator |
| Keyword(3) | renewal equation |
| Keyword(4) | Fredholm determinant |
| Keyword(5) | zeta function |
| Keyword(6) | Cantor set |
| 1st Author's Name | Makoto Mori |
| 1st Author's Affiliation | Dept.Math.College of Humanities and Sciences, Nihon University() |
| Date | 1998/3/12 |
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| Volume (vol) | vol.97 |
| Number (no) | 591 |
| Page | pp.pp.- |
| #Pages | 7 |
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