Conformal Graph Directed Markov Systems on Carnot Groups

Released on by Vasileios Chousionis
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  • Conformal Graph Directed Markov Systems on Carnot Groups Book Detail

  • Author : Vasileios Chousionis
  • Release Date : 2020-09-28
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 153
  • ISBN 13 : 1470442159
  • File Size : 31,31 MB
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Conformal Graph Directed Markov Systems on Carnot Groups by Vasileios Chousionis PDF Summary

Book 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.

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