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020 a| 9781470442156q| (paperback);

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084 a| 30L10a| 53C17a| 37C40a| 11J70a| 28A78a| 37B10a| 37C30a| 37D35a| 37F35a| 47H102| msc;

100 1 a| Chousionis, Vasilionis,d| 1980-?| UNAUTHORIZED;

245 10 a| Conformal graph directed Markov systems on Carnot groupsh| [electronic resource] /c| Vasilis Chousionis, Jeremy Tyson, Mariusz Urbanski.;

260 a| Providence, RI :b| American Mathematical Society,c| [2020];

300 a| viii, 155 pages ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1291.;

500 a| "Forthcoming, volume 266, number 1291.";

504 a| Includes bibliographical references and index.;

505 0 a| 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.;

506 a| Available only to authorized users.;

520 a| "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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Nilpotent Lie groups.=| ^A267945;

650 0 a| Conformal mapping.=| ^A57278;

650 0 a| Markov processes.=| ^A27090;

650 0 a| Hausdorff measures.=| ^A65793;

650 0 a| Thermodynamicsx| Mathematical models.=| ^A1037372;

650 7 a| Functions of a complex variable {For analysis on manifolds, see 58-XX} -- Analysis on metric spaces -- Quasiconformal mappings in metric spaces.2| msc;

650 7 a| 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 bund2| msc;

650 7 a| 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, inv2| msc;

650 7 a| Number theory -- Diophantine approximation, transcendental number theory [See also 11K60] -- Continued fractions and generalizations [See also 11A55, 11K50].2| msc;

650 7 a| Measure and integration {For analysis on manifolds, see 58-XX} -- Classical measure theory -- Hausdorff and packing measures.2| msc;

650 7 a| 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].2| msc;

650 7 a| 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,2| msc;

650 7 a| 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 dimensi2| msc;

650 7 a| 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].2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Tyson, Jeremy T.,d| 1972-?| UNAUTHORIZED;

700 1 a| Urbański, Mariusz.=| ^A561134;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6346625;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5643350-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 7/19/2021x| EBOOKz| JERESOURCE;

Conformal graph directed Markov systems on Carnot groups / Vasilis Chousionis, Jeremy Tyson, Mariusz Urbanski.

Author/creator	Chousionis, Vasilionis, 1980-
Other author	Tyson, Jeremy T., 1972-
Other author	Urbański, Mariusz.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2020]
Description	viii, 155 pages ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Nilpotent Lie groups. Conformal mapping. Markov processes. Hausdorff measures. Thermodynamics--Mathematical models.

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.
Abstract	"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.
General note	"Forthcoming, volume 266, number 1291."
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2020032014
ISBN	9781470442156 (paperback)
ISBN	(pdf)

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Conformal graph directed Markov systems on Carnot groups / Vasilis Chousionis, Jeremy Tyson, Mariusz Urbanski.

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