Ergodic Theory via Joinings

Author: Eli Glasner

Publisher: American Mathematical Soc.

ISBN: 1470419513

Category:

Page: 384

View: 9231

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

Author: Joseph Auslander,Aimee Johnson,Cesar E. Silva

Publisher: American Mathematical Soc.

ISBN: 1470422999

Category: Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Non-Archimedean Fatou and Julia sets

Page: 316

View: 7574

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.
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Ergodic Theory and Dynamical Systems

Author: Yves Coudène

Publisher: Springer

ISBN: 1447172876

Category: Mathematics

Page: 190

View: 6653

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.
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Ergodic Theory

Independence and Dichotomies

Author: David Kerr,Hanfeng Li

Publisher: Springer

ISBN: 3319498479

Category: Mathematics

Page: 431

View: 7843

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.
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DCDS-A

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 9144

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An Introduction to Infinite Ergodic Theory

Author: Jon Aaronson

Publisher: American Mathematical Soc.

ISBN: 9780821804940

Category: Mathematics

Page: 284

View: 9806

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 behavior, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible ``ergodic behavior'' 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.
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An Introduction to Infinite Ergodic Theory

Author: Jon Aaronson

Publisher: American Mathematical Soc.

ISBN: 9780821804940

Category: Mathematics

Page: 284

View: 2780

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 behavior, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible ``ergodic behavior'' 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.
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Theorie der Gleichverteilung

Author: Edmund Hlawka

Publisher: N.A

ISBN: N.A

Category: Distribution, Uniform (Probability theory)

Page: 142

View: 2617

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Maß- und Integrationstheorie

Author: Jürgen Elstrodt

Publisher: Springer-Verlag

ISBN: 3662579391

Category: Mathematics

Page: 464

View: 7273

Das Lehrbuch vermittelt solides Basiswissen zu den thematischen Schwerpunkten Produktmaße, Fourier-Transformation, Transformationsformel, Konvergenzbegriffe, absolute Stetigkeit und Maße auf topologischen Räumen. Höhepunkte sind die Herleitung des Riesz’schen Darstellungssatzes und der Beweis der Existenz und Eindeutigkeit des Haar’schen Maßes. Der Band enthält ferner mathematikhistorische Ausflüge und Kurzporträts von Mathematikern, die zum Thema des Buchs wichtige Beiträge geliefert haben, sowie zahlreiche Übungsaufgaben zur Vertiefung des Stoffs.
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Zufälligkeit und Wahrscheinlichkeit

Eine algorithmische Begründung der Wahrscheinlichkeitstheorie

Author: Claus P. Schnorr

Publisher: Springer-Verlag

ISBN: 3540368833

Category: Mathematics

Page: 212

View: 6894

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Automorphe Formen

Author: Anton Deitmar

Publisher: Springer-Verlag

ISBN: 3642123902

Category: Mathematics

Page: 252

View: 2338

Das Buch bietet eine Einführung in die Theorie der automorphen Formen. Beginnend bei klassischen Modulformen führt der Autor seine Leser hin zur modernen, darstellungstheoretischen Beschreibung von automorphen Formen und ihren L-Funktionen. Das Hauptgewicht legt er auf den Übergang von der klassischen, elementaren Sichtweise zu der modernen, durch die Darstellungstheorie begründete Herangehensweise. Diese Art der Verbindung von klassischer und moderner Sichtweise war in der Lehrbuchliteratur bisher nicht zu finden.
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Spectral Synthesis

Author: John J. Benedetto

Publisher: Springer-Verlag

ISBN: 3322966615

Category: Technology & Engineering

Page: 281

View: 4640

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Dimensionstheorie

Author: Karl Menger

Publisher: Springer-Verlag

ISBN: 3663160564

Category: Mathematics

Page: 324

View: 6419

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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