研究課題/領域番号 |
15H06416
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研究機関 | 島根大学 |
研究代表者 |
イェーリッシュ ヨハネス 島根大学, 総合理工学研究科(研究院), 講師 (90741869)
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研究期間 (年度) |
2015-08-28 – 2017-03-31
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キーワード | エルゴード理論 |
研究実績の概要 |
Several results have been obtained which are stronger and in greater generality than expected. The revision of the paper Dynamics of infinitely generated nicely expanding rational semigroups and the inducing method (with H. Sumi) has been completed and the paper has been accepted for publication in the Transactions of the AMS, which contributes to establishing the thermodynamic formalism for expanding rational semigroups. Further main results: On the regularity of complex Takagi functions and random complex dynamical systems (preprint with H. Sumi), and on critical exponents of normal subgroups of free groups (joint with K.Matsuzaki, preprint submitted). Also, on critical exponents of normal subgroups of Gromov hyperbolic groups (preprint with K.Matsuzaki and Y. Yabuki).
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現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
Several results have been obtained which are stronger and in greater generality than expected (e.g. Hoelder regularity of higher-order complex Takagi functions.)
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今後の研究の推進方策 |
(A) Critical exponents of subgroups of Kleinian groups and Gromov hyperbolic groups. We investigate how this exponent changes when passing to a subgroup.To study this problem, we consider skew product extensions of topological Markov chains by infinite graphs. We study the topological pressure in for these dynamical systems, which has applications to critical exponents of subgroups of Kleinian groups. Further tasks are to investigate the multifractal formalism for cusp windings, and the Laplacian for Cayley graphs.
(B) Dynamics of semigroups of rational maps on the Riemann sphere and random compelex dynamics. We consider Takagi functions for expanding interval maps satisfying the open set condition, and seek to generalise previous results on the Riemann sphere.
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備考 |
My recent preprints and publications are available on the above webpage.
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