
Conformal Graph Directed Markov Systems on Carnot Groups
American Mathematical Society (Publisher)
Published on 30. October 2020
Book
Paperback/Softback
153 pages
978-1-4704-4215-6 (ISBN)
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
313 gr
ISBN-13
978-1-4704-4215-6 (9781470442156)
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Schweitzer Classification
Persons
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
Jeremy T. Tyson, University of Illinois at Urbana-Champaign, IL
Mariusz Urbanski, University of North Texas, Denton, TX