Abstract
We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincaré exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum.
| Original language | English |
|---|---|
| Pages (from-to) | 849-883 |
| Number of pages | 35 |
| Journal | Ergodic Theory and Dynamical Systems |
| Volume | 45 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2025 Mar |
Keywords
- Bowen-Series map
- Fuchsian group
- multifractal analysis
- thermodynamic formalism
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics