Description 
1 online resource (viii, 170 pages) 
Series 
Memoirs of the American Mathematical Society, 00659266 ; number 1291 
Contents 
Carnot groups  Carnot groups of Iwasawa type and conformal mappings  Metric and geometric properties of conformal maps  Conformal graph directed Markov systems  Examples of GDMS in Carnot groups  Countable alphabet symbolic dynamics : foundations of the thermodynamic formalism  Hausdorff dimension of limit sets  Conformal measures and regularity of domains  Examples revisited  Finer properties of limit sets : Hausdorff, packing and invariant measures  Equivalent separation conditions for finite GDMS 
Summary 
"We develop a comprehensive theory of conformal graph directed Markov systems in the nonRiemannian setting of Carnot groups equipped with a subRiemannian metric. In particular, we 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. We illustrate our results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such subRiemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the nonreal classical rank one hyperbolic spaces" Provided by publisher 
Notes 
"Forthcoming, volume 266, number 1291." 
Bibliography 
Includes bibliographical references and index 
Notes 
Description basaed on print version record 
Subject 
Nilpotent Lie groups.


Conformal mapping.


Markov processes.


Hausdorff measures.


Thermodynamics  Mathematical models


Markov Chains


Conformal mapping


Hausdorff measures


Markov processes


Nilpotent Lie groups


Thermodynamics  Mathematical models


Functions of a complex variable {For analysis on manifolds, see 58XX}  Analysis on metric spaces  Quasiconformal mappings in metric spaces.


Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx}  Global differential geometry [See also 51H25, 58XX; for related bund.


Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70XX]  Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]  Smooth ergodic theory, inv.


Number theory  Diophantine approximation, transcendental number theory [See also 11K60]  Continued fractions and generalizations [See also 11A55, 11K50].


Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70XX]  Topological dynamics [See also 54H20]  Symbolic dynamics [See also 37Cxx, 37Dxx].


Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70XX]  Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]  Zeta functions, (RuelleFr.


Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70XX]  Dynamical systems with hyperbolic behavior  Thermodynamic formalism, variational principles.


Measure and integration {For analysis on manifolds, see 58XX}  Classical measure theory  Hausdorff and packing measures.


Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70XX]  Complex dynamical systems [See also 30D05, 32H50]  Conformal densities and Hausdorff dimensi.


Operator theory  Nonlinear operators and their properties {For global and geometric aspects, see 49J53, 58XX, especially 58Cxx}  Fixedpoint theorems [See also 37C25, 54H25, 55M20, 58C30].

Form 
Electronic book

Author 
Tyson, Jeremy T., 1972 author.


Urbański, Mariusz, author.

ISBN 
1470462451 

9781470462451 
