| 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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| 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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