2020 Fiscal Year Annual Research Report
Thermodynamic formalism for non-compact spaces with applications in conformal dynamics
| Project/Area Number |
17K14203
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| Research Institution | Nagoya University |
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Principal Investigator |
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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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | Ergodic Theory / Thermodynamic formalism / Fractal geometry / Group extensions |
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| Outline of Annual Research Achievements |
We have partially extended and revised our results on the multifractal analysis of cusp windings of the geodesic flow on hyperbolic surfaces. The paper has been accepted in Stochastics and Dynamics (with M. Kesseboehmer and S. Munday).
We have partially extended and revised our results on mixed multi fractal Birkhoff spectra for non-uniformly expanding one-dimensional Markov maps. We found new phenomena caused by the interaction of parabolic generators with infinitely many hyperbolic generators. In particular, we found that for the arithmetic mean spectrum of the backward continued fraction map, every non-empty level set has full Hausdorff dimension. The paper has been accepted in Advances in Mathematics (with H. Takahasi).
For graph extensions of Markov shifts we further investigated the interplay between the thermodynamic formalism for the base dynamics and the extended system using the method of inducing (with M. Stadlbauer). The special case of Z-extensions was studied with M. Groeger and M. Kesseboehmer.
We made the first steps to develop thermodynamic formalism for infinitely generated Fuchsian groups. We extend the theory of graph-directed Markov systems and pseudo-Markov systems. This is an ongoing project with M. Urbanski.
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