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Author : M. Denker
Publisher : Springer
ISBN 13 : 3540382631
Total Pages : 367 pages
Book Rating : 4.5/5 (43 download)
Download or read book Ergodic Theory on Compact Spaces written by M. Denker and published by Springer. This book was released on 2006-11-14 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. Denker
Publisher :
ISBN 13 : 9783662170120
Total Pages : 372 pages
Book Rating : 4.1/5 (71 download)
Download or read book Ergodic Theory on Compact Spaces written by M. Denker and published by . This book was released on 2014-01-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Manfred Denker
Publisher : Springer
ISBN 13 : 9780387077970
Total Pages : 360 pages
Book Rating : 4.0/5 (779 download)
Download or read book Ergodic Theory on Compact Spaces written by Manfred Denker and published by Springer. This book was released on 1976 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mark Pollicott
Publisher : Cambridge University Press
ISBN 13 : 9780521435932
Total Pages : 176 pages
Book Rating : 4.4/5 (359 download)
Download or read book Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds written by Mark Pollicott and published by Cambridge University Press. This book was released on 1993-02-04 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes provide a unique introduction to Pesin theory and its applications.
Author : Peter Walters
Publisher : Springer Science & Business Media
ISBN 13 : 9780387951522
Total Pages : 268 pages
Book Rating : 4.9/5 (515 download)
Download or read book An Introduction to Ergodic Theory written by Peter Walters and published by Springer Science & Business Media. This book was released on 2000-10-06 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces. Several examples are detailed, and the final chapter outlines results and applications of ergodic theory to other branches of mathematics.
Author : Cesar E. Silva
Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.0/5 (716 download)
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
Author : William Parry
Publisher : Cambridge University Press
ISBN 13 : 9780521604901
Total Pages : 128 pages
Book Rating : 4.6/5 (49 download)
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.
Author : Manfred Einsiedler
Publisher : Springer Science & Business Media
ISBN 13 : 0857290215
Total Pages : 486 pages
Book Rating : 4.8/5 (572 download)
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.
Author : Karma Dajani
Publisher : CRC Press
ISBN 13 : 1000402770
Total Pages : 268 pages
Book Rating : 4.0/5 (4 download)
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.
Author : Ricardo Mañé
Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (321 download)
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.
Author : Tanja Eisner
Publisher : Springer
ISBN 13 : 3319168983
Total Pages : 630 pages
Book Rating : 4.3/5 (191 download)
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
Author : Jon Aaronson
Publisher : American Mathematical Soc.
ISBN 13 : 0821804944
Total Pages : 298 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Paul R. Halmos
Publisher : Courier Dover Publications
ISBN 13 : 0486826848
Total Pages : 113 pages
Book Rating : 4.4/5 (868 download)
Download or read book Lectures on Ergodic Theory written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2017-11-15 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise classic by a well-known master of mathematical exposition covers recurrence, ergodic theorems, ergodicity and mixing properties, and the relation between conjugacy and equivalence. 1956 edition.
Author : Mark Pollicott
Publisher : Cambridge University Press
ISBN 13 : 9780521575997
Total Pages : 198 pages
Book Rating : 4.5/5 (759 download)
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).
Author : Ricardo Mane
Publisher : Springer Science & Business Media
ISBN 13 : 3642703356
Total Pages : 328 pages
Book Rating : 4.6/5 (427 download)
Download or read book Ergodic Theory and Differentiable Dynamics written by Ricardo Mane and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 328 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.
Author : David Kerr
Publisher : Springer
ISBN 13 : 3319498479
Total Pages : 455 pages
Book Rating : 4.3/5 (194 download)
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.
Author : Mariusz Urbański
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110702681
Total Pages : 458 pages
Book Rating : 4.1/5 (17 download)
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.
