Graph Directed Markov Systems

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Conformal Graph Directed Markov Systems On Carnot Groups

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Author : Vasileios Chousionis
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Conformal Graph Directed Markov Systems On Carnot Groups written by Vasileios Chousionis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.

The authors 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, they 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. They illustrate their 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.

Graph Directed Markov Systems

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Author : R. Daniel Mauldin
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-07

Graph Directed Markov Systems written by R. Daniel Mauldin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-07 with Mathematics categories.

The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students.

Graph Directed Markov Systems

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Author : R. Daniel Mauldin
language : en
Publisher:
Release Date : 2014-05-14

Graph Directed Markov Systems written by R. Daniel Mauldin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Electronic books categories.

Monograph on Graph Directed Markov Systems with backgound and research level material.

Dimension Spectrum And Graph Directed Markov Systems

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Author :
language : en
Publisher:
Release Date : 2006

Dimension Spectrum And Graph Directed Markov Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Graph theory categories.

Resonances For Graph Directed Markov Systems And Geometry Of Infinitely Generated Dynamical Systems

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Author : Martial R. Hille
language : en
Publisher:
Release Date : 2009

Resonances For Graph Directed Markov Systems And Geometry Of Infinitely Generated Dynamical Systems written by Martial R. Hille and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Graph theory categories.

Asymptotic Counting In Conformal Dynamical Systems

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Author : Mark Pollicott
language : en
Publisher: American Mathematical Society
Release Date : 2021-09-24

Asymptotic Counting In Conformal Dynamical Systems written by Mark Pollicott and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-24 with Mathematics categories.

View the abstract.

Open Conformal Systems And Perturbations Of Transfer Operators

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Author : Mark Pollicott
language : en
Publisher: Springer
Release Date : 2018-02-05

Open Conformal Systems And Perturbations Of Transfer Operators written by Mark Pollicott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.

The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, rational functions and meromorphic maps. Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.

Finer Thermodynamic Formalism Distance Expanding Maps And Countable State Subshifts Of Finite Type Conformal Gdmss Lasota Yorke Maps And Fractal Geometry

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Author : Mariusz Urbański
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-06-06

Finer Thermodynamic Formalism Distance Expanding Maps And Countable State Subshifts Of Finite Type Conformal Gdmss Lasota Yorke Maps And Fractal Geometry written by Mariusz Urbański and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-06 with Mathematics categories.

This book consists of three volumes. The first volume contains introductory accounts of topological dynamical systems, fi nite-state symbolic dynamics, distance expanding maps, and ergodic theory of metric dynamical systems acting on probability measure spaces, including metric entropy theory of Kolmogorov and Sinai. More advanced topics comprise infi nite ergodic theory, general thermodynamic formalism, topological entropy and pressure. Thermodynamic formalism of distance expanding maps and countable-alphabet subshifts of fi nite type, graph directed Markov systems, conformal expanding repellers, and Lasota-Yorke maps are treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal systems. Multifractal analysis and real analyticity of pressure are also covered. The third volume is devoted to the study of dynamics, ergodic theory, thermodynamic formalism and fractal geometry of rational functions of the Riemann sphere.

Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps

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Author : Mariusz Urbański
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22

Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps written by Mariusz Urbański and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.

The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature.

Weakly Modular Graphs And Nonpositive Curvature

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Author : Jérémie Chalopin
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18

Weakly Modular Graphs And Nonpositive Curvature written by Jérémie Chalopin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.

This article investigates structural, geometrical, and topological characteri-zations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various “nonpositive cur-vature” and “local-to-global” properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a far-reaching common generalization of median graphs (and more generally, of mod-ular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under different disguises (1–skeletons, collinearity graphs, covering graphs, domains, etc.) in several seemingly-unrelated fields of mathematics: * Metric graph theory * Geometric group theory * Incidence geometries and buildings * Theoretical computer science and combinatorial optimization We give a local-to-global characterization of weakly modular graphs and their sub-classes in terms of simple connectedness of associated triangle-square complexes and specific local combinatorial conditions. In particular, we revisit characterizations of dual polar graphs by Cameron and by Brouwer-Cohen. We also show that (disk-)Helly graphs are precisely the clique-Helly graphs with simply connected clique complexes. With l1–embeddable weakly modular and sweakly modular graphs we associate high-dimensional cell complexes, having several strong topological and geometrical properties (contractibility and the CAT(0) property). Their cells have a specific structure: they are basis polyhedra of even 􀀁–matroids in the first case and orthoscheme complexes of gated dual polar subgraphs in the second case. We resolve some open problems concerning subclasses of weakly modular graphs: we prove a Brady-McCammond conjecture about CAT(0) metric on the orthoscheme.