Scaling functions for graph directed Markov systems

Daniel Ingebretson

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arXiv · 1901.04067

Scaling functions for graph directed Markov systems

Daniel Ingebretson

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Abstract

We introduce the scaling function associated to a graph directed Markov system, and show that it is a H\"{o}lder continuous function of the dual symbolic Cantor set. With some natural separation and regularity conditions, each such system has a unique Cantor limit set in Euclidean space. We prove that the scaling function is a complete invariant of $ C^{1+\alpha} $ conjugacy between limit sets. We conclude by relating the scaling function to the pressure, and discussing several applications to the dimension theory of limit sets.

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BibTeX RIS

Daniel Ingebretson. 2019-01-13. Scaling functions for graph directed Markov systems. https://arxiv.org/abs/1901.04067

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