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arXiv · 1801.04034

Hausdorff dimension of Kuperberg minimal sets

Daniel Ingebretson
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Abstract

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 minimal set. We develop new techniques to study the symbolic dynamics and dimension theory of this minimal set, by relating it to the limit set of a graph directed pseudo-Markov system over a countable alphabet.

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Daniel Ingebretson. 2018-01-12. Hausdorff dimension of Kuperberg minimal sets. https://arxiv.org/abs/1801.04034

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