Multifractal Analysis of F-exponents for Finitely Irreducible Conformal Graph Directed Markov Systems
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917907931332608 |
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| author | Dalaklis, Nathan |
| author_facet | Dalaklis, Nathan |
| contents | Let $Φ= \{ϕ_e\}_{e\in E}$ be a finitely irreducible conformal graph directed Markov system (CGDMS) with symbolic representation $E_A^{\infty}$ and limit set $J$. Under a mild condition on the system, we give a multifractal analysis of level sets of Birkhoff averages with respect to Hausdorff dimension for a large family of functions. We then apply these results to a few examples in the case of both $E$ finite and $E$ countably infinite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multifractal Analysis of F-exponents for Finitely Irreducible Conformal Graph Directed Markov Systems Dalaklis, Nathan Dynamical Systems 37D35, 28A80, 28D20 (Primary) 37A50, 37A05 (Secondary) Let $Φ= \{ϕ_e\}_{e\in E}$ be a finitely irreducible conformal graph directed Markov system (CGDMS) with symbolic representation $E_A^{\infty}$ and limit set $J$. Under a mild condition on the system, we give a multifractal analysis of level sets of Birkhoff averages with respect to Hausdorff dimension for a large family of functions. We then apply these results to a few examples in the case of both $E$ finite and $E$ countably infinite. |
| title | Multifractal Analysis of F-exponents for Finitely Irreducible Conformal Graph Directed Markov Systems |
| topic | Dynamical Systems 37D35, 28A80, 28D20 (Primary) 37A50, 37A05 (Secondary) |
| url | https://arxiv.org/abs/2404.09348 |