Conformal graph directed Markov systems on Carnot groups /

"We 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, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Chousionis, Vasilionis, 1980- (Author), Tyson, Jeremy T., 1972- (Author), Urbański, Mariusz (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence, RI : American Mathematical Society, [2020]
Series:Memoirs of the American Mathematical Society, number 1291
Subjects:
Nilpotent Lie groups.
Conformal mapping.
Markov processes.
Hausdorff measures.
Thermodynamics > Mathematical models.
Markov Chains
Groupes de Lie nilpotents.
Applications conformes.
Processus de Markov.
Mesures de Hausdorff.
Thermodynamique > Modèles mathématiques.
Grupos de Lie
Hausdorff, Medidas de
Teoría ergódica
Markov, Procesos de
Conformal mapping
Hausdorff measures
Markov processes
Nilpotent Lie groups
Thermodynamics > Mathematical models
Functions of a complex variable {For analysis on manifolds, see 58-XX} > 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, 58-XX; for related bund.
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] > 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].
Measure and integration {For analysis on manifolds, see 58-XX} > Classical measure theory > Hausdorff and packing measures.
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] > 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, 70-XX] > Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx] > Zeta functions, (Ruelle-Fr.
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] > Dynamical systems with hyperbolic behavior > Thermodynamic formalism, variational principles.
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] > 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, 58-XX, especially 58Cxx} > Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30].
Online Access:Texto completo
Table of 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.

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