| 研究課題/領域番号 |
21K03269
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| 研究種目 |
基盤研究(C)
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| 配分区分 | 基金 |
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| 応募区分 | 一般 |
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| 審査区分 |
小区分12010:基礎解析学関連
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| 研究機関 | 名古屋大学 |
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研究代表者 |
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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| 研究期間 (年度) |
2021-04-01 – 2025-03-31
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| 研究課題ステータス |
交付 (2023年度)
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| 配分額 *注記 |
4,030千円 (直接経費: 3,100千円、間接経費: 930千円)
2023年度: 1,300千円 (直接経費: 1,000千円、間接経費: 300千円)
2022年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
2021年度: 1,300千円 (直接経費: 1,000千円、間接経費: 300千円)
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| キーワード | 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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| 研究開始時の研究の概要 |
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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| 研究実績の概要 |
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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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
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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| 今後の研究の推進方策 |
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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