| Description |
1 online resource (viii, 170 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; 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 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 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 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"-- 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.
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Conformal mapping.
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Markov processes.
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Hausdorff measures.
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Thermodynamics -- Mathematical models
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Markov Chains
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Conformal mapping
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Hausdorff measures
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Markov processes
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Nilpotent Lie groups
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Thermodynamics -- Mathematical models
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Functions of a complex variable {For analysis on manifolds, see 58-XX} -- Analysis on metric spaces -- Quasiconformal mappings in metric spaces.
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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.
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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.
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Number theory -- Diophantine approximation, transcendental number theory [See also 11K60] -- Continued fractions and generalizations [See also 11A55, 11K50].
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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].
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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.
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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.
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Measure and integration {For analysis on manifolds, see 58-XX} -- Classical measure theory -- Hausdorff and packing measures.
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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.
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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].
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| Form |
Electronic book
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| Author |
Tyson, Jeremy T., 1972- author.
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Urbański, Mariusz, author.
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| ISBN |
1470462451 |
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9781470462451 |
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