Non Invertible Dynamical Systems Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps

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Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps

Author : Mariusz Urbański
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110702681
Total Pages : 458 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps by : Mariusz Urbański

Download or read book Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps written by Mariusz Urbański and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ergodic Theory - Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps

Author : Mariusz Urbański
Publisher : de Gruyter
ISBN 13 : 9783110702644
Total Pages : 0 pages
Book Rating : 4.7/5 (26 download)

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Book Synopsis Ergodic Theory - Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps by : Mariusz Urbański

Download or read book Ergodic Theory - Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps written by Mariusz Urbański and published by de Gruyter. This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains detailed treatment of thermodynamic formalism. Topological pressure, entropy, variational principle, and equilibrium states are presented in detail in the first volume. Abstract ergodic theory is also given a significant attention.

Non-invertible Dynamical Systems: Ergodic theory : finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps

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Author : Mariusz Urbański
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (22 download)

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Book Synopsis Non-invertible Dynamical Systems: Ergodic theory : finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps by : Mariusz Urbański

Download or read book Non-invertible Dynamical Systems: Ergodic theory : finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps written by Mariusz Urbański and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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." --Provided by publisher.

Thermodynamic Formalism and Applications to Dimension Theory

Author : Luis Barreira
Publisher : Birkhäuser
ISBN 13 : 9783034803366
Total Pages : 300 pages
Book Rating : 4.8/5 (33 download)

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Book Synopsis Thermodynamic Formalism and Applications to Dimension Theory by : Luis Barreira

Download or read book Thermodynamic Formalism and Applications to Dimension Theory written by Luis Barreira and published by Birkhäuser. This book was released on 2013-11-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.

Ergodic Theory and Differentiable Dynamics

Author : Ricardo Mane
Publisher : Springer
ISBN 13 : 9783642703379
Total Pages : 0 pages
Book Rating : 4.7/5 (33 download)

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Book Synopsis Ergodic Theory and Differentiable Dynamics by : Ricardo Mane

Download or read book Ergodic Theory and Differentiable Dynamics written by Ricardo Mane and published by Springer. This book was released on 2011-11-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.

Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

Author : Luis Barreira
Publisher : Springer
ISBN 13 : 9783642280894
Total Pages : 290 pages
Book Rating : 4.2/5 (88 download)

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Book Synopsis Ergodic Theory, Hyperbolic Dynamics and Dimension Theory by : Luis Barreira

Download or read book Ergodic Theory, Hyperbolic Dynamics and Dimension Theory written by Luis Barreira and published by Springer. This book was released on 2012-04-29 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.

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
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311070269X
Total Pages : 524 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Finer Thermodynamic Formalism – Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota-Yorke Maps and Fractal Geometry by : Mariusz Urbański

Download or read book 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 published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-05-23 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Finer Thermodynamic Formalism - Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota-Yorke Maps and Fractal Geometry

Author : Mariusz Mario Sara Urbański Roy Munday
Publisher : de Gruyter
ISBN 13 : 9783110700619
Total Pages : 0 pages
Book Rating : 4.7/5 (6 download)

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Book Synopsis Finer Thermodynamic Formalism - Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota-Yorke Maps and Fractal Geometry by : Mariusz Mario Sara Urbański Roy Munday

Download or read book Finer Thermodynamic Formalism - Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota-Yorke Maps and Fractal Geometry written by Mariusz Mario Sara Urbański Roy Munday and published by de Gruyter. This book was released on 2022-05-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains detailed treatment of thermodynamic formalism. Distance expanding maps and Lasota-Yorke maps of an interval are then treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal

Ergodic Theory

Author : Idris Assani
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311046151X
Total Pages : 148 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Ergodic Theory by : Idris Assani

Download or read book Ergodic Theory written by Idris Assani and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-06-20 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit directions of a vector cocycle, remarks and examples Optimal norm approximation in ergodic theory The iterated Prisoner’s Dilemma: good strategies and their dynamics Lyapunov exponents for conservative twisting dynamics: a survey Takens’ embedding theorem with a continuous observable

Topics in Dynamics and Ergodic Theory

Author : Sergey Bezuglyi
Publisher : Cambridge University Press
ISBN 13 : 9780521533652
Total Pages : 276 pages
Book Rating : 4.5/5 (336 download)

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Book Synopsis Topics in Dynamics and Ergodic Theory by : Sergey Bezuglyi

Download or read book Topics in Dynamics and Ergodic Theory written by Sergey Bezuglyi and published by Cambridge University Press. This book was released on 2003-12-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.

Infinite Ergodic Theory of Numbers

Author : Marc Kesseböhmer
Publisher : de Gruyter
ISBN 13 : 9783110439410
Total Pages : 0 pages
Book Rating : 4.4/5 (394 download)

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Book Synopsis Infinite Ergodic Theory of Numbers by : Marc Kesseböhmer

Download or read book Infinite Ergodic Theory of Numbers written by Marc Kesseböhmer and published by de Gruyter. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: By connecting dynamical systems and number theory this graduate textbook on ergodic theory covers a highly active area of mathematics, where a variety of strands of research open up. After introducing number-theoretical dynamical systems, the text t

Ergodic Theory and Dynamical Systems

Author : Yves Coudène
Publisher : Springer
ISBN 13 : 1447172876
Total Pages : 192 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Ergodic Theory and Dynamical Systems by : Yves Coudène

Download or read book Ergodic Theory and Dynamical Systems written by Yves Coudène and published by Springer. This book was released on 2016-11-10 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

Ergodic Theory

Author : Cesar E. Silva
Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva and published by Springer Nature. This book was released on 2023-07-31 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

Ergodic Theory and Differentiable Dynamics

Author : Ricardo Mañé
Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Ergodic Theory and Differentiable Dynamics by : Ricardo Mañé

Download or read book Ergodic Theory and Differentiable Dynamics written by Ricardo Mañé and published by Springer. This book was released on 1987 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to ergodic theory, with an emphasis on its relationship with the theory of differentiable dynamical systems, sometimes called differentiable ergodic theory. The first chapter a quick review of measure theory is included as a reference.

Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby

Author : Joseph Auslander
Publisher : American Mathematical Soc.
ISBN 13 : 1470422999
Total Pages : 336 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby by : Joseph Auslander

Download or read book Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby written by Joseph Auslander and published by American Mathematical Soc.. This book was released on 2016-11-29 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of three conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby Centennial Conference, held from October 30–31, 2010, at Bryn Mawr College; the Williams Ergodic Theory Conference, held from July 27–29, 2012, at Williams College; and the AMS Special Session on Ergodic Theory and Symbolic Dynamics, held from January 17–18, 2014, in Baltimore, MD. This volume contains articles covering a variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.

Dynamical Systems and Ergodic Theory

Author : Mark Pollicott
Publisher : Cambridge University Press
ISBN 13 : 9780521575997
Total Pages : 198 pages
Book Rating : 4.5/5 (759 download)

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Book Synopsis Dynamical Systems and Ergodic Theory by : Mark Pollicott

Download or read book Dynamical Systems and Ergodic Theory written by Mark Pollicott and published by Cambridge University Press. This book was released on 1998-01-29 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).

Ergodic Optimization in the Expanding Case

Author : Eduardo Garibaldi
Publisher : Springer
ISBN 13 : 3319666436
Total Pages : 76 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Ergodic Optimization in the Expanding Case by : Eduardo Garibaldi

Download or read book Ergodic Optimization in the Expanding Case written by Eduardo Garibaldi and published by Springer. This book was released on 2017-09-21 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the interpretation of ergodic optimal problems as questions of variational dynamics, employing a comparable approach to that of the Aubry-Mather theory for Lagrangian systems. Ergodic optimization is primarily concerned with the study of optimizing probability measures. This work presents and discusses the fundamental concepts of the theory, including the use and relevance of Sub-actions as analogues to subsolutions of the Hamilton-Jacobi equation. Further, it provides evidence for the impressively broad applicability of the tools inspired by the weak KAM theory.