Hyperbolic graphs: critical regularity and box dimension
Dynamical Systems
2017-02-22 v1
Abstract
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.
Cite
@article{arxiv.1702.06416,
title = {Hyperbolic graphs: critical regularity and box dimension},
author = {Lorenzo J. Díaz and Katrin Gelfert and Maik Gröger and Tobias Jäger},
journal= {arXiv preprint arXiv:1702.06416},
year = {2017}
}
Comments
48 pages, 11 figures