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Conformal Graph Directed Markov Systems on Carnot Groups
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Conformal Graph Directed Markov Systems on Carnot Groups
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Conformal Graph Directed Markov Systems on Carnot Groups
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eBook
Conformal Graph Directed Markov Systems on Carnot Groups
2020
Overview
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
Publisher
American Mathematical Society
Subject
ISBN
9781470442156, 1470442159
