Hyperbolic graphs: Critical regularity and box dimension
Copyright policy )Hyperbolic graphs: Critical regularity and box dimension
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��lder 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.
48 pages, 11 figures
invariant graph, Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), hyperbolicity, box dimension, Dimension theory of smooth dynamical systems, 37C45, 37D20, 37D35, 37D30, Dynamical Systems (math.DS), skew product, fibered blender, Dynamical systems involving maps of trees and graphs, FOS: Mathematics, Thermodynamic formalism, variational principles, equilibrium states for dynamical systems, topological pressure, Mathematics - Dynamical Systems, Partially hyperbolic systems and dominated splittings
invariant graph, Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), hyperbolicity, box dimension, Dimension theory of smooth dynamical systems, 37C45, 37D20, 37D35, 37D30, Dynamical Systems (math.DS), skew product, fibered blender, Dynamical systems involving maps of trees and graphs, FOS: Mathematics, Thermodynamic formalism, variational principles, equilibrium states for dynamical systems, topological pressure, Mathematics - Dynamical Systems, Partially hyperbolic systems and dominated splittings
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