Conformal Graph Directed Markov Systems on Carnot Groups
Vasileios Chousionis; Jeremy T. Tyson; Mariusz Urbanski
AMERICAN MATHEMATICAL SOCIETY
2020
pokkari
Develops 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, the authors develop the thermodynamic formalism and show that the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter.