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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2312.08974 |
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| _version_ | 1866913247484968960 |
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| author | Rutar, Alex |
| author_facet | Rutar, Alex |
| contents | We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode the parametric geometry of the Lagrange dual associated with the constrained variational principle. We also give a direct derivation of the Hausdorff dimension of the level sets of the upper and lower local dimensions by exploiting certain weak uniformity properties of the space of Bernoulli measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08974 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multifractal analysis via Lagrange duality Rutar, Alex Dynamical Systems 28A80, 37C45 (Primary) 49N15, 94A17, 60F10 (Secondary) We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode the parametric geometry of the Lagrange dual associated with the constrained variational principle. We also give a direct derivation of the Hausdorff dimension of the level sets of the upper and lower local dimensions by exploiting certain weak uniformity properties of the space of Bernoulli measures. |
| title | Multifractal analysis via Lagrange duality |
| topic | Dynamical Systems 28A80, 37C45 (Primary) 49N15, 94A17, 60F10 (Secondary) |
| url | https://arxiv.org/abs/2312.08974 |