A multifractal analysis for escaping trajectories on free groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911257847660544 |
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| author | Liu, Ziyu |
| author_facet | Liu, Ziyu |
| contents | We consider a free group extension of a subshift of finite type $σ:Σ\rightarrowΣ$, and consider three sets of points in $Σ$ to which the corresponding trajectories on the free group escape to a given point in the Gromov boundary of the free group in three different senses. Under very mild conditions, we provide a common positive lower bound for the $u$-dimensions of these three sets. We also show that the lower bound is equal to the $u$-dimensions of these three sets when the extension and $u$ have certain symmetries. Moreover, we apply our results to geodesic flows on free group covers of Schottky surfaces, and show that there exists a dimension gap between the three sets we considered and the entire escaping set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A multifractal analysis for escaping trajectories on free groups Liu, Ziyu Dynamical Systems 37B10, 37D20, 37D40, 37F32, 37C45 We consider a free group extension of a subshift of finite type $σ:Σ\rightarrowΣ$, and consider three sets of points in $Σ$ to which the corresponding trajectories on the free group escape to a given point in the Gromov boundary of the free group in three different senses. Under very mild conditions, we provide a common positive lower bound for the $u$-dimensions of these three sets. We also show that the lower bound is equal to the $u$-dimensions of these three sets when the extension and $u$ have certain symmetries. Moreover, we apply our results to geodesic flows on free group covers of Schottky surfaces, and show that there exists a dimension gap between the three sets we considered and the entire escaping set. |
| title | A multifractal analysis for escaping trajectories on free groups |
| topic | Dynamical Systems 37B10, 37D20, 37D40, 37F32, 37C45 |
| url | https://arxiv.org/abs/2511.06980 |