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math.DS2019
Scaling functions for graph directed Markov systems
Daniel Ingebretson
We introduce the scaling function associated to a graph directed Markov system, and show that it is a Hölder continuous function of the dual symbolic Cantor set. With some natural…
math.DS2018
Dimension rigidity for cookie-cutter Cantor sets
Daniel Ingebretson
We show that two cookie-cutter Cantor sets with the same symbolic coding are differentiably equivalent if and only if their Hausdorff dimensions are equal.
math.DS2018
Hausdorff dimension of Kuperberg minimal sets
Daniel Ingebretson
In 1994, Kuperberg constructed a smooth flow on a three-manifold with no periodic orbits. It was later shown that a generic Kuperberg flow preserves a codimension one laminar minim…