2017 Fiscal Year Research-status Report
Thermodynamic formalism for non-compact spaces with applications in conformal dynamics
| Project/Area Number |
17K14203
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| Research Institution | Shimane University |
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Principal Investigator |
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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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | Dynamical Systems / Transience / Thermodynamic Formalism |
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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The proposed formalism for Z extensions has been successfully developed.
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| Strategy for Future Research Activity |
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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| Causes of Carryover |
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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| Remarks |
The webpage contains information about my research.
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