| Project/Area Number |
21K03269
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Nagoya University |
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Principal Investigator |
イェーリッシュ ヨハネス 名古屋大学, 多元数理科学研究科, 准教授 (90741869)
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| Project Period (FY) |
2021-04-01 – 2025-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2023: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2022: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2021: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ergodic theory / thermodynamic formalism / large deviations / multifractal analysis / amenable graphs / Fuchsian groups / Hausdorff dimension / Large deviations / Ergodic theory / Fractal geometry / Multifractal analysis / Non-uniformly hyperbolic / Ergodic Theory / Fractal Geometry |
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| Outline of Research at the Start |
We develop the ergodic theory and its applications to fractal geometry for conformal dynamical systems which are non-uniformly hyperbolic or whose state space is not compact. The main examples are Kleinian groups, semigroups of rational maps on the Riemann sphere, and Markov interval maps.
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| Outline of Annual Research Achievements |
We focused on the ergodic theory for dynamical systems with weak forms of hyperbolicity, and applications to fractal geometry and geometric group theory. In relation to (A3, B2) of the research plan, we established a large deviation principle and multifractal formalism for Lyapunov exponents for the Bowen-Series map associated with a Fuchsian group with even corners (joint preprint with H. Takahasi, Keio U). In relation to (B3), we established Bowen’s formula for the Hausdorff dimension of Julia sets of rational graph directed Markov systems (joint preprint with H. Sumi, Kyoto U, T. Watanabe, Chubu U, and T. Arimitsu, Nagoya U) . In relation (A3, B1), we obtained new results on the spectral radius of graph extensions of Markov shifts (joint preprint with M. Stadlbauer, E. Rocha).
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Research on several topics made very good progress. However, project (A1) with M. Kesseboehmer (U Bremen) and M. Groeger (Jagiellonian U), and project (A2) with M. Urbanski (U North Texas) are slightly delayed.
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| Strategy for Future Research Activity |
We plan to complete the delayed projects with M. Kesseboehmer (U Bremen) and M. Groeger (Jagiellonian U), and M. Urbanski (U North Texas) in 2024. The projects are about transient interval maps related to random walks, and infinitely generated Schottky groups. We plan to visit U Bremen and U North Texas.
We work on follow-up projects with H Takahasi (Keio U) on backward continued fraction expansions. We work on follow-up projects with M. Stadlbauer on amenable graph extensions of countable Markov shifts. We proceed to investigate the Julia sets of rational graph directed Markov systems.
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