A First Course In Ergodic Theory

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A First Course In Ergodic Theory

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Author : Karma Dajani
language : en
Publisher: CRC Press
Release Date : 2021-07-04

A First Course In Ergodic Theory written by Karma Dajani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-04 with Mathematics categories.

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.

Dynamical Systems And Ergodic Theory

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Author : Mark Pollicott
language : en
Publisher:
Release Date : 2013-07-13

Dynamical Systems And Ergodic Theory written by Mark Pollicott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-13 with categories.

Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.

A First Course In Information Theory

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Author : Raymond W. Yeung
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

A First Course In Information Theory written by Raymond W. Yeung and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

A First Course in Information Theory is an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.

The Ergodic Theory Of Discrete Sample Paths

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Author : Paul C. Shields
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

The Ergodic Theory Of Discrete Sample Paths written by Paul C. Shields 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 1996 with Mathematics categories.

This book is about finite-alphabet stationary processes, which are important in physics, engineering, and data compression. The focus is on the combinatorial properties of typical finite sample paths drawn from a stationary, ergodic process. A primary goal, only partially realized, is to develop a theory based directly on sample path arguments with minimal appeals to the probability formalism. A secondary goal is to give a careful presentation of the many models for stationary finite-alphabet processes that have been developed in probability theory, ergodic theory, and information theory.

Introduction To Smooth Ergodic Theory

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Author : Luís Barreira
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-19

Introduction To Smooth Ergodic Theory written by Luís Barreira 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 2023-05-19 with Mathematics categories.

This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided. In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.

Ergodic Theory

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Author : Cesar E. Silva
language : en
Publisher: Springer Nature
Release Date : 2023-07-31

Ergodic Theory written by Cesar E. Silva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.

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

Invitation To Ergodic Theory

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Author : César Ernesto Silva
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Invitation To Ergodic Theory written by César Ernesto Silva 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 2008 with Mathematics categories.

"Several examples of a dynamical system are developed in detail to illustrate various dynamical concepts. These include in particular the baker's transformation, irrational rotations, the dyadic odometer, the Hajian-Kakutani transformation, the Gauss transformation, and the Chacon transformation. There is a detailed discussion of cutting and stacking transformations in ergodic theory. The book includes several exercises and some open questions to give the flavor of current research. The book also introduces some notions from topological dynamics, such as minimality, transitivity and symbolic spaces; and develops some metric topology, including the Baire category theorem."--BOOK JACKET.

A First Course In Functional Analysis

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Author : Orr Moshe Shalit
language : en
Publisher: CRC Press
Release Date : 2017-03-16

A First Course In Functional Analysis written by Orr Moshe Shalit and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Mathematics categories.

Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.

A First Course In Information Theory

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Author : Raymond W. Yeung
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-30

A First Course In Information Theory written by Raymond W. Yeung and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-30 with Computers categories.

An introduction to information theory for discrete random variables. Classical topics and fundamental tools are presented along with three selected advanced topics. Yeung (Chinese U. of Hong Kong) presents chapters on information measures, zero-error data compression, weak and strong typicality, the I-measure, Markov structures, channel capacity, rate distortion theory, Blahut-Arimoto algorithms, information inequalities, and Shannon-type inequalities. The advanced topics included are single-source network coding, multi-source network coding, and entropy and groups. Annotation copyrighted by Book News, Inc., Portland, OR.

The Mathematical Foundations Of Mixing

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Author : Rob Sturman
language : en
Publisher: Cambridge University Press
Release Date : 2006-09-21

The Mathematical Foundations Of Mixing written by Rob Sturman 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 2006-09-21 with Mathematics categories.

Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions.