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Conformal Graph Directed Markov Systems on Carnot Groups
Vasileios Chousionis
Jeremy T. Tyson
Mariusz Urbanski
出版
American Mathematical Soc.
, 2020-09-28
主題
Mathematics / General
ISBN
1470442159
9781470442156
URL
http://books.google.com.hk/books?id=-un_DwAAQBAJ&hl=&source=gbs_api
EBook
SAMPLE
註釋
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.