| 研究課題/領域番号 |
17K14203
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| 研究機関 | 島根大学 |
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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, 講師 (90741869)
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| 研究期間 (年度) |
2017-04-01 – 2020-03-31
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| キーワード | Dynamical Systems / Transience / Thermodynamic Formalism |
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| 研究実績の概要 |
We developed a thermodynamic formalism for skew-periodic Z-extensions of expanding interval maps with finitely many full branches. Our new formalism allows us to perform a dimensional analysis of the recurrent dynamics, as well as the transient dynamics with prescribed escape rate. We obtain explicit formulae for dimension gaps caused by transience. We also discuss the relation to Z-extensions of Kleinian groups. This is a joint work with Maik Groeger (Univ. Vienna) and Marc Kesseboehmer (Univ. Bremen).We are planning to submit a preprint containing the above results within a few weeks.
The joint paper with Hiroki Sumi (Kyoto Univ.) on complex analogues of the Takagi function and random complex dynamics has been accepted for publication by Advances in Mathematics.
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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
The proposed formalism for Z extensions has been successfully developed.
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| 今後の研究の推進方策 |
We proceed according to our original plans. Next, we study the thermodynamic formalism for non-uniformly hyperbolic semigroups of rational maps on the Riemann sphere.Moreover,in addition to our original plans, several new ideas arose from the results obtained in the previous year.
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| 次年度使用額が生じた理由 |
The amount to be used in the next fiscal year is caused by a delayed computer purchase.
The usage plan is to purchase the computer in the next fiscal year (30年度).
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| 備考 |
The webpage contains information about my research.
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