A First Course In Ergodic Theory

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A First Course in Ergodic Theory

Karma Dajani,Charlene Kalle
A First Course in Ergodic Theory Book PDF

Author : Karma Dajani,Charlene Kalle
Publisher : CRC Press
Page : 268 pages
File Size : 51,6 Mb
Release : 2021-07-04
Category : Mathematics
ISBN : 9781000402773

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A First Course in Ergodic Theory by Karma Dajani,Charlene Kalle Pdf

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.

Lectures on Ergodic Theory

Paul R. Halmos
Lectures on Ergodic Theory Book PDF

Author : Paul R. Halmos
Publisher : Courier Dover Publications
Page : 113 pages
File Size : 52,7 Mb
Release : 2017-12-13
Category : Mathematics
ISBN : 9780486814896

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Lectures on Ergodic Theory by Paul R. Halmos Pdf

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.

Basic Ergodic Theory

Mahendra Ganpatrao Nadkarni
Basic Ergodic Theory Book PDF

Author : Mahendra Ganpatrao Nadkarni
Publisher : Birkhauser
Page : 168 pages
File Size : 50,5 Mb
Release : 1998
Category : Mathematics
ISBN : UOM:39015046892025

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Basic Ergodic Theory by Mahendra Ganpatrao Nadkarni Pdf

This is an introductory book on ergodic theory. The presentation has a slow pace and the book can be read by anyone with a background in basic measure theory and metric topology. In particular, the first two chapters, the elements of ergodic theory, can form a course of four to six lectures at the advanced undergraduate or the beginning graduate level. A new feature of the book is that the basic topics of ergodic theory such as the Poincar recurrence lemma, induced automorphisms and Kakutani towers, compressibility and E. Hopf's theorem, the theorem of Ambrose on representation of flows are treated at the descriptive set-theoretic level before their measure-theoretic or topological versions are presented. In addition, topics centering around the Glimm-Effros theorem are discussed, topics which have so far not found a place in texts on ergodic theory. In this second edition, a section on rank one automorphisms and a brief discussion of the ergodic theorem due to Wiener and Wintner have been added. "This relatively short book is, for anyone new to ergodic theory, admirably broad in scope. The exposition is clear, and the brevity of the book has not been achieved by giving terse proofs. The examples have been chosen with great care. Historical facts and many references serve to help connect the reader with literature that goes beyond the content of the book as well as explaining how the subject developed. It is easy to recommend this book for students as well as anyone who would like to learn about the descriptive approach to ergodic theory." (Summary of a review of the first edition in Math Reviews)

A First Course in Functional Analysis

Orr Moshe Shalit
A First Course in Functional Analysis Book PDF

Author : Orr Moshe Shalit
Publisher : CRC Press
Page : 257 pages
File Size : 41,5 Mb
Release : 2017-03-16
Category : Mathematics
ISBN : 9781498771627

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A First Course in Functional Analysis by Orr Moshe Shalit Pdf

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.

Ergodic Theory

Karl E. Petersen,Karl Petersen
Ergodic Theory Book PDF

Author : Karl E. Petersen,Karl Petersen
Publisher : Cambridge University Press
Page : 348 pages
File Size : 54,7 Mb
Release : 1989-11-23
Category : Mathematics
ISBN : 0521389976

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Ergodic Theory by Karl E. Petersen,Karl Petersen Pdf

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.

One-Dimensional Ergodic Schrödinger Operators

David Damanik,Jake Fillman
One Dimensional Ergodic Schr dinger Operators Book PDF

Author : David Damanik,Jake Fillman
Publisher : American Mathematical Society
Page : 464 pages
File Size : 52,6 Mb
Release : 2022-08-18
Category : Mathematics
ISBN : 9781470456061

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One-Dimensional Ergodic Schrödinger Operators by David Damanik,Jake Fillman Pdf

The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks. Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrödinger operators with dynamically defined potentials. It also includes a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics. This text is accessible to graduate students who have completed one-semester courses in measure theory and complex analysis. It is intended to serve as an introduction to the field for junior researchers and beginning graduate students as well as a reference text for people already working in this area. It is well suited for self-study and contains numerous exercises (many with hints).

A First Course in Fractional Sobolev Spaces

Giovanni Leoni
A First Course in Fractional Sobolev Spaces Book PDF

Author : Giovanni Leoni
Publisher : American Mathematical Society
Page : 605 pages
File Size : 48,5 Mb
Release : 2023-04-12
Category : Mathematics
ISBN : 9781470468989

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A First Course in Fractional Sobolev Spaces by Giovanni Leoni Pdf

This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the right-hand side in a fractional Sobolev space and some basic properties of the fractional Laplacian. The first part of the book is accessible to advanced undergraduates with a strong background in integration theory; the second part, to graduate students having familiarity with measure and integration and some functional analysis. Basic knowledge of Sobolev spaces would help, but is not necessary. The book can also serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines with a solid mathematics background. It contains several exercises and is self-contained.

A First Course in Rational Continuum Mechanics

Anonim
A First Course in Rational Continuum Mechanics Book PDF

Author : Anonim
Publisher : Academic Press
Page : 388 pages
File Size : 50,6 Mb
Release : 1992-02-03
Category : Mathematics
ISBN : 0080873871

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A First Course in Rational Continuum Mechanics by Anonim Pdf

A First Course in Rational Continuum Mechanics V1

A First Course in Rational Continuum Mechanics

C. Truesdell
A First Course in Rational Continuum Mechanics Book PDF

Author : C. Truesdell
Publisher : Elsevier
Page : 304 pages
File Size : 46,6 Mb
Release : 2016-06-03
Category : Technology & Engineering
ISBN : 9781483220482

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A First Course in Rational Continuum Mechanics by C. Truesdell Pdf

A First Course in Rational Continuum Mechanics, Volume 1: General Concepts describes general concepts in rational continuum mechanics and covers topics ranging from bodies and forces to motions and energies, kinematics, and the stress tensor. Constitutive relations are also discussed, and some definitions and theorems of algebra, geometry, and calculus are included. Exercises and their solutions are given as well. Comprised of four chapters, this volume begins with an introduction to rational mechanics by focusing on the mathematical concepts of bodies, forces, motions, and energies. Systems that provide possible universes for mechanics are described. The next chapter explores kinematics, with emphasis on bodies, placements, and motions as well as other relevant concepts like local deformation and homogeneous transplacement. The book also considers the stress tensor and Cauchy's fundamental theorem before concluding with a discussion on constitutive relations. This monograph is designed for students taking a course in mathematics or physics.

An Introduction to Ergodic Theory

Peter Walters
An Introduction to Ergodic Theory Book PDF

Author : Peter Walters
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 54,9 Mb
Release : 2000-10-06
Category : Mathematics
ISBN : 0387951520

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An Introduction to Ergodic Theory by Peter Walters Pdf

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.

Introduction to Smooth Ergodic Theory

Luís Barreira,Yakov Pesin
Introduction to Smooth Ergodic Theory Book PDF

Author : Luís Barreira,Yakov Pesin
Publisher : American Mathematical Society
Page : 355 pages
File Size : 40,8 Mb
Release : 2023-04-28
Category : Mathematics
ISBN : 9781470473075

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Introduction to Smooth Ergodic Theory by Luís Barreira,Yakov Pesin Pdf

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.

Topological and Ergodic Theory of Symbolic Dynamics

Henk Bruin
Topological and Ergodic Theory of Symbolic Dynamics Book PDF

Author : Henk Bruin
Publisher : American Mathematical Society
Page : 481 pages
File Size : 52,8 Mb
Release : 2023-01-20
Category : Mathematics
ISBN : 9781470469849

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Topological and Ergodic Theory of Symbolic Dynamics by Henk Bruin Pdf

Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.

A First Course in Information Theory

Raymond W. Yeung
A First Course in Information Theory Book PDF

Author : Raymond W. Yeung
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781441986085

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A First Course in Information Theory by Raymond W. Yeung Pdf

This book provides 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.

Fundamentals of Measurable Dynamics

Daniel J. Rudolph
Fundamentals of Measurable Dynamics Book PDF

Author : Daniel J. Rudolph
Publisher : Oxford University Press, USA
Page : 190 pages
File Size : 44,8 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015019619942

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Fundamentals of Measurable Dynamics by Daniel J. Rudolph Pdf

This book is designed to provide graduate students and other researchers in dynamical systems theory with an introduction to the ergodic theory of Lebesgue spaces. The author's aim is to present a technically complete account which offers an in-depth understanding of the techniques of the field, both classical and modern. Thus, the basic structure theorems of Lebesgue spaces are given in detail as well as complete accounts of the ergodic theory of a single transformation, ergodic theorems, mixing properties and entropy. Subsequent chapters extend the earlier material to the areas of joinings and representation theorems, in particular the theorems of Ornstein and Krieger. Prerequisites are a working knowledge of Lebesgue measure and the topology of the real line as might be gained from the first year of a graduate course. Many exercises and examples are included to illustrate and to further cement the reader's understanding of the material. The result is a text which will furnish the reader with a sound technical background from the foundations of the subject to some of its most recent developments.

Topics in Harmonic Analysis and Ergodic Theory

Joseph Rosenblatt
Topics in Harmonic Analysis and Ergodic Theory Book PDF

Author : Joseph Rosenblatt
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 48,8 Mb
Release : 2007
Category : Ergodic theory
ISBN : 9780821842355

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Topics in Harmonic Analysis and Ergodic Theory by Joseph Rosenblatt Pdf

There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. This text presents a series of essays on the topic.