Conformal Graph Directed Markov Systems on Carnot Groups - Couverture souple

Chousionis, Vasileios; Tyson, Jeremy T.; Urbanski, Mariusz

 
9781470442156: Conformal Graph Directed Markov Systems on Carnot Groups
Couverture souple
ISBN 10 : 1470442159 ISBN 13 : 9781470442156
Editeur : 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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À propos de l?auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2020
Langue
anglais
ISBN 10 
1470442159
ISBN 13 
9781470442156
Reliure
Broché
Nombre de pages
153
Coordonnées du fabricant
non disponible
Personne responsable
non disponible