Conformal Graph Directed Markov Systems on Carnot Groups (Memoirs of the American Mathematical Society)

About the Author Vasileios Chousionis, University of Connecticut, Storrs, CT Jeremy T. Tyson, University of Illinois at Urbana-Champaign, ILMariusz Urbanski, University of North Texas, Denton, TX Product Description The authors 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, they 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. They illustrate their 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.