2020 Fiscal Year Final Research Report
Thermodynamic formalism for non-compact spaces with applications in conformal dynamics
| Project/Area Number |
17K14203
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University (2019-2020)
Shimane University (2017-2018) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | Ergodic Theory / Dynamical Systems / Fractal Geometry / Random walks / Multifractal analysis |
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| Outline of Final Research Achievements |
We investigated ergodic theory and thermodynamic formalism for topological Markov chains with countably many symbols, and non-uniformly expanding conformal dynamical systems. Examples include Markov interval maps and geodesic flows on hyperbolic surfaces with cusps. Our main focus was the interplay of dynamics and fractal-geometry of associated invariant sets. We performed a multifractal analysis of Birkhoff averages, cusp windings, local dimensions of Gibbs measures, and harmonic functions.
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| Free Research Field |
Ergodic theory, Fractal geometry
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| Academic Significance and Societal Importance of the Research Achievements |
Chaos in dynamical systems and the intricate geometry of fractal sets are fascinating for everyone. These phenomena have resulted in mathematical research of highest level over the past 50 years. In our project, we worked on some of the recent trends in these fields.
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