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

Vasileios Chousionis (author), Jeremy T. Tyson (author) & Mariusz Urbanski (author)

 
9781470442156: Conformal Graph Directed Markov Systems on Carnot Groups (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 1470442159 ISBN 13: 9781470442156
Publisher: American Mathematical Society, 2020

Synopsis

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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About the Author

Vasileios Chousionis, University of Connecticut, Storrs, CT

Jeremy T. Tyson, University of Illinois at Urbana-Champaign, IL

Mariusz Urbanski, University of North Texas, Denton, TX

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2020
Language
English
ISBN 10 
1470442159
ISBN 13 
9781470442156
Binding
Paperback
Number of pages
153