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Conformal Graph Directed Markov Systems on Carnot Groups.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society SeriesPublisher: Providence : American Mathematical Society, 2020Copyright date: ©2020Edition: 1st edDescription: 1 online resource (170 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470462451
Subject(s): Genre/Form: Additional physical formats: Print version:: Conformal Graph Directed Markov Systems on Carnot GroupsDDC classification:
  • 621.40210000000002
LOC classification:
  • TJ265 .C468 2020
Online resources:
Contents:
Cover -- Title page -- Introduction -- Chapter 1. Carnot groups -- 1.1. Carnot groups -- 1.2. Contact mappings -- 1.3. Dimension comparison in Carnot groups -- Chapter 2. Carnot groups of Iwasawa type and conformal mappings -- 2.1. Iwasawa groups of complex, quaternionic or octonionic type -- 2.2. Conformal mappings on Carnot groups -- Chapter 3. Metric and geometric properties of conformal maps -- 3.1. Norm of the horizontal differential and local Lipschitz constant -- 3.2. Koebe distortion theorems for Carnot conformal mappings -- Chapter 4. Conformal graph directed Markov systems -- 4.1. Graph Directed Markov Systems -- 4.2. Carnot conformal graph directed Markov systems -- Chapter 5. Examples of GDMS in Carnot groups -- 5.1. Infinite self-similar iterated function systems -- 5.2. Iwasawa conformal Cantor sets -- 5.3. Continued fractions in Iwasawa groups -- 5.4. Complex hyperbolic Kleinian groups of Schottky type -- Chapter 6. Countable alphabet symbolic dynamics: foundations of the thermodynamic formalism -- 6.1. Subshifts of finite type and topological pressure -- 6.2. Gibbs states, equilibrium states and potentials -- 6.3. Perron-Frobenius Operator -- Chapter 7. Hausdorff dimension of limit sets -- 7.1. Topological pressure, -number, and Bowen's parameter -- 7.2. Hausdorff dimension and Bowen's formula -- 7.3. Characterizations of co-finitely regular and strongly regular Carnot conformal IFS -- 7.4. Dimension spectrum for subsystems of Carnot conformal IFS -- Chapter 8. Conformal measures and regularity of domains -- 8.1. Bounding coding type and null boundary -- 8.2. Regularity properties of domains in Carnot groups -- 8.3. Conformal measure estimates -- Chapter 9. Examples revisited -- 9.1. Infinite self-similar iterated function systems -- 9.2. Continued fractions in groups of Iwasawa type -- 9.3. Iwasawa conformal Cantor sets.
Chapter 10. Finer properties of limit sets: Hausdorff, packing and invariant measures -- 10.1. Finiteness of Hausdorff measure and positivity of packing measure -- 10.2. Positivity of Hausdorff measure and finiteness of packing measure -- 10.3. Hausdorff and packing measures for continued fraction systems in groups of Iwasawa type -- 10.4. Hausdorff dimensions of invariant measures -- Chapter 11. Equivalent separation conditions for finite GDMS -- Bibliography -- Index -- Back Cover.
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Cover -- Title page -- Introduction -- Chapter 1. Carnot groups -- 1.1. Carnot groups -- 1.2. Contact mappings -- 1.3. Dimension comparison in Carnot groups -- Chapter 2. Carnot groups of Iwasawa type and conformal mappings -- 2.1. Iwasawa groups of complex, quaternionic or octonionic type -- 2.2. Conformal mappings on Carnot groups -- Chapter 3. Metric and geometric properties of conformal maps -- 3.1. Norm of the horizontal differential and local Lipschitz constant -- 3.2. Koebe distortion theorems for Carnot conformal mappings -- Chapter 4. Conformal graph directed Markov systems -- 4.1. Graph Directed Markov Systems -- 4.2. Carnot conformal graph directed Markov systems -- Chapter 5. Examples of GDMS in Carnot groups -- 5.1. Infinite self-similar iterated function systems -- 5.2. Iwasawa conformal Cantor sets -- 5.3. Continued fractions in Iwasawa groups -- 5.4. Complex hyperbolic Kleinian groups of Schottky type -- Chapter 6. Countable alphabet symbolic dynamics: foundations of the thermodynamic formalism -- 6.1. Subshifts of finite type and topological pressure -- 6.2. Gibbs states, equilibrium states and potentials -- 6.3. Perron-Frobenius Operator -- Chapter 7. Hausdorff dimension of limit sets -- 7.1. Topological pressure, -number, and Bowen's parameter -- 7.2. Hausdorff dimension and Bowen's formula -- 7.3. Characterizations of co-finitely regular and strongly regular Carnot conformal IFS -- 7.4. Dimension spectrum for subsystems of Carnot conformal IFS -- Chapter 8. Conformal measures and regularity of domains -- 8.1. Bounding coding type and null boundary -- 8.2. Regularity properties of domains in Carnot groups -- 8.3. Conformal measure estimates -- Chapter 9. Examples revisited -- 9.1. Infinite self-similar iterated function systems -- 9.2. Continued fractions in groups of Iwasawa type -- 9.3. Iwasawa conformal Cantor sets.

Chapter 10. Finer properties of limit sets: Hausdorff, packing and invariant measures -- 10.1. Finiteness of Hausdorff measure and positivity of packing measure -- 10.2. Positivity of Hausdorff measure and finiteness of packing measure -- 10.3. Hausdorff and packing measures for continued fraction systems in groups of Iwasawa type -- 10.4. Hausdorff dimensions of invariant measures -- Chapter 11. Equivalent separation conditions for finite GDMS -- Bibliography -- Index -- Back Cover.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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