Ergodic Theorems

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Ergodic Theorems

Author : Ulrich Krengel
Publisher : Walter de Gruyter
ISBN 13 : 3110844648
Total Pages : 369 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Ergodic Theorems by : Ulrich Krengel

Download or read book Ergodic Theorems written by Ulrich Krengel and published by Walter de Gruyter. This book was released on 2011-03-01 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Ergodic Theorems for Group Actions

Author : A.A. Tempelman
Publisher : Springer Science & Business Media
ISBN 13 : 9401714606
Total Pages : 418 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Ergodic Theorems for Group Actions by : A.A. Tempelman

Download or read book Ergodic Theorems for Group Actions written by A.A. Tempelman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to generalizations of the classical Birkhoff and von Neuman ergodic theorems to semigroup representations in Banach spaces, semigroup actions in measure spaces, homogeneous random fields and random measures on homogeneous spaces. The ergodicity, mixing and quasimixing of semigroup actions and homogeneous random fields are considered as well. In particular homogeneous spaces, on which all homogeneous random fields are quasimixing are introduced and studied (the n-dimensional Euclidean and Lobachevsky spaces with n>=2, and all simple Lie groups with finite centre are examples of such spaces. Also dealt with are applications of general ergodic theorems for the construction of specific informational and thermodynamical characteristics of homogeneous random fields on amenable groups and for proving general versions of the McMillan, Breiman and Lee-Yang theorems. A variational principle which characterizes the Gibbsian homogeneous random fields in terms of the specific free energy is also proved. The book has eight chapters, a number of appendices and a substantial list of references. For researchers whose works involves probability theory, ergodic theory, harmonic analysis, measure theory and statistical Physics.

Ergodic Theory

Author : Manfred Einsiedler
Publisher : Springer Science & Business Media
ISBN 13 : 0857290215
Total Pages : 486 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Ergodic Theory by : Manfred Einsiedler

Download or read book Ergodic Theory written by Manfred Einsiedler and published by Springer Science & Business Media. This book was released on 2010-09-11 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

Ergodic Theory and Statistical Mechanics

Author : Jean Moulin Ollagnier
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Ergodic Theory and Statistical Mechanics by : Jean Moulin Ollagnier

Download or read book Ergodic Theory and Statistical Mechanics written by Jean Moulin Ollagnier and published by Lecture Notes in Mathematics. This book was released on 1985-03 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ergodic Theory via Joinings

Author : Eli Glasner
Publisher : American Mathematical Soc.
ISBN 13 : 1470419513
Total Pages : 402 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ergodic Theory via Joinings by : Eli Glasner

Download or read book Ergodic Theory via Joinings written by Eli Glasner and published by American Mathematical Soc.. This book was released on 2015-01-09 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces modern ergodic theory. It emphasizes a new approach that relies on the technique of joining two (or more) dynamical systems. This approach has proved to be fruitful in many recent works, and this is the first time that the entire theory is presented from a joining perspective. Another new feature of the book is the presentation of basic definitions of ergodic theory in terms of the Koopman unitary representation associated with a dynamical system and the invariant mean on matrix coefficients, which exists for any acting groups, amenable or not. Accordingly, the first part of the book treats the ergodic theory for an action of an arbitrary countable group. The second part, which deals with entropy theory, is confined (for the sake of simplicity) to the classical case of a single measure-preserving transformation on a Lebesgue probability space.

An Introduction to Infinite Ergodic Theory

Author : Jon Aaronson
Publisher : American Mathematical Soc.
ISBN 13 : 0821804944
Total Pages : 298 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis An Introduction to Infinite Ergodic Theory by : Jon Aaronson

Download or read book An Introduction to Infinite Ergodic Theory written by Jon Aaronson and published by American Mathematical Soc.. This book was released on 1997 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behaviour, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behaviour" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.

Ergodic Theory of Random Transformations

Author : Yuri Kifer
Publisher : Birkhäuser
ISBN 13 : 9781468491777
Total Pages : 210 pages
Book Rating : 4.4/5 (917 download)

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Book Synopsis Ergodic Theory of Random Transformations by : Yuri Kifer

Download or read book Ergodic Theory of Random Transformations written by Yuri Kifer and published by Birkhäuser. This book was released on 2012-06-02 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ergodic theory of dynamical systems i.e., the qualitative analysis of iterations of a single transformation is nowadays a well developed theory. In 1945 S. Ulam and J. von Neumann in their short note [44] suggested to study ergodic theorems for the more general situation when one applies in turn different transforma tions chosen at random. Their program was fulfilled by S. Kakutani [23] in 1951. 'Both papers considered the case of transformations with a common invariant measure. Recently Ohno [38] noticed that this condition was excessive. Ergodic theorems are just the beginning of ergodic theory. Among further major developments are the notions of entropy and characteristic exponents. The purpose of this book is the study of the variety of ergodic theoretical properties of evolution processes generated by independent applications of transformations chosen at random from a certain class according to some probability distribution. The book exhibits the first systematic treatment of ergodic theory of random transformations i.e., an analysis of composed actions of independent random maps. This set up allows a unified approach to many problems of dynamical systems, products of random matrices and stochastic flows generated by stochastic differential equations.

Operator Theoretic Aspects of Ergodic Theory

Author : Tanja Eisner
Publisher : Springer
ISBN 13 : 3319168983
Total Pages : 630 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Operator Theoretic Aspects of Ergodic Theory by : Tanja Eisner

Download or read book Operator Theoretic Aspects of Ergodic Theory written by Tanja Eisner and published by Springer. This book was released on 2015-11-18 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory

Ergodic Theory and Differentiable Dynamics

Author : Ricardo Mañé
Publisher : Springer Science & Business Media
ISBN 13 : 9783540152781
Total Pages : 317 pages
Book Rating : 4.1/5 (527 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 Science & Business Media. This book was released on 1987-01 with total page 317 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 and Semisimple Groups

Author : R.J. Zimmer
Publisher : Springer Science & Business Media
ISBN 13 : 1468494880
Total Pages : 219 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Ergodic Theory and Semisimple Groups by : R.J. Zimmer

Download or read book Ergodic Theory and Semisimple Groups written by R.J. Zimmer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course given at the University of Chicago in 1980-81. As with the course, the main motivation of this work is to present an accessible treatment, assuming minimal background, of the profound work of G. A. Margulis concerning rigidity, arithmeticity, and structure of lattices in semi simple groups, and related work of the author on the actions of semisimple groups and their lattice subgroups. In doing so, we develop the necessary prerequisites from earlier work of Borel, Furstenberg, Kazhdan, Moore, and others. One of the difficulties involved in an exposition of this material is the continuous interplay between ideas from the theory of algebraic groups on the one hand and ergodic theory on the other. This, of course, is not so much a mathematical difficulty as a cultural one, as the number of persons comfortable in both areas has not traditionally been large. We hope this work will also serve as a contribution towards improving that situation. While there are a number of satisfactory introductory expositions of the ergodic theory of integer or real line actions, there is no such exposition of the type of ergodic theoretic results with which we shall be dealing (concerning actions of more general groups), and hence we have assumed absolutely no knowledge of ergodic theory (not even the definition of "ergodic") on the part of the reader. All results are developed in full detail.

Lectures on Ergodic Theory

Author : Paul R. Halmos
Publisher : Courier Dover Publications
ISBN 13 : 0486814890
Total Pages : 113 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Lectures on Ergodic Theory by : Paul R. Halmos

Download or read book Lectures on Ergodic Theory written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2017-12-13 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented." Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.

Ergodic Theory

Author : David Kerr
Publisher : Springer
ISBN 13 : 3319498479
Total Pages : 455 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Ergodic Theory by : David Kerr

Download or read book Ergodic Theory written by David Kerr and published by Springer. This book was released on 2017-02-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.

Ergodic Theory

Author : Karl E. Petersen
Publisher : Cambridge University Press
ISBN 13 : 9780521389976
Total Pages : 348 pages
Book Rating : 4.3/5 (899 download)

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Book Synopsis Ergodic Theory by : Karl E. Petersen

Download or read book Ergodic Theory written by Karl E. Petersen and published by Cambridge University Press. This book was released on 1989-11-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.

Eigenvalues, Inequalities, and Ergodic Theory

Author : Mu-Fa Chen
Publisher : Springer Science & Business Media
ISBN 13 : 1846281237
Total Pages : 239 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Eigenvalues, Inequalities, and Ergodic Theory by : Mu-Fa Chen

Download or read book Eigenvalues, Inequalities, and Ergodic Theory written by Mu-Fa Chen and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use

A First Course in Ergodic Theory

Author : Karma Dajani
Publisher : CRC Press
ISBN 13 : 1000402770
Total Pages : 268 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis A First Course in Ergodic Theory by : Karma Dajani

Download or read book A First Course in Ergodic Theory written by Karma Dajani and published by CRC Press. This book was released on 2021-07-04 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Ergodic Theory provides readers with an introductory course in Ergodic Theory. This textbook has been developed from the authors’ own notes on the subject, which they have been teaching since the 1990s. Over the years they have added topics, theorems, examples and explanations from various sources. The result is a book that is easy to teach from and easy to learn from — designed to require only minimal prerequisites. Features Suitable for readers with only a basic knowledge of measure theory, some topology and a very basic knowledge of functional analysis Perfect as the primary textbook for a course in Ergodic Theory Examples are described and are studied in detail when new properties are presented.

Topics in Ergodic Theory

Author : William Parry
Publisher : Cambridge University Press
ISBN 13 : 9780521604901
Total Pages : 128 pages
Book Rating : 4.6/5 (49 download)

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Book Synopsis Topics in Ergodic Theory by : William Parry

Download or read book Topics in Ergodic Theory written by William Parry and published by Cambridge University Press. This book was released on 2004-06-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to topics and examples of ergodic theory, a central area of pure mathematics.

Convergence in Ergodic Theory and Probability

Author : Vitaly Bergelson
Publisher : Walter de Gruyter
ISBN 13 : 3110889382
Total Pages : 461 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Convergence in Ergodic Theory and Probability by : Vitaly Bergelson

Download or read book Convergence in Ergodic Theory and Probability written by Vitaly Bergelson and published by Walter de Gruyter. This book was released on 2011-06-15 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.