Hyperbolic graphs: critical regularity and box dimension
| Autor: | Lorenzo J. Díaz, Maik Gröger, Katrin Gelfert, Tobias Jäger |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Mathematics::Dynamical Systems Applied Mathematics General Mathematics 010102 general mathematics Dimension (graph theory) Minkowski–Bouligand dimension 37C45 37D20 37D35 37D30 Dynamical Systems (math.DS) Lipschitz continuity Effective dimension 01 natural sciences Cantor set Fractal Attractor FOS: Mathematics Mathematics - Dynamical Systems 0101 mathematics Invariant (mathematics) Mathematics |
| DOI: | 10.48550/arxiv.1702.06416 |
| Popis: | We study fractal properties of invariant graphs of hyperbolic and partially hyperbolic skew product diffeomorphisms in dimension three. We describe the critical (either Lipschitz or at all scales H\"older continuous) regularity of such graphs. We provide a formula for their box dimension given in terms of appropriate pressure functions. We distinguish three scenarios according to the base dynamics: Anosov, one-dimensional attractor, or Cantor set. A key ingredient for the dimension arguments in the latter case will be the presence of a so-called fibered blender. Comment: 48 pages, 11 figures |
| Databáze: | OpenAIRE |
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