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Lectures on Ergodic Theory

Lectures on Ergodic Theory Author Paul R. Halmos
ISBN-10 9780486814896
Release 2017-12-13
Pages 112
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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.



Lectures on Ergodic Theory

Lectures on Ergodic Theory Author Paul R. Halmos
ISBN-10 9780486826844
Release 2017-11-15
Pages 112
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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.



Lectures on Ergodic Theory

Lectures on Ergodic Theory Author Paul Richard Halmos
ISBN-10 9780821841259
Release 1956
Pages 99
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This classic book is based on lectures given by the author at the University of Chicago in 1956. The topics covered include, in particular, recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. There is also a general discussion of the relation between conjugacy and equivalence. With minimal prerequisites of some analysis and measure theory, this work can be used for a one-semester course in ergodic theory or for self-study.



Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds Author Mark Pollicott
ISBN-10 0521435935
Release 1993-02-04
Pages 162
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These lecture notes provide a unique introduction to Pesin theory and its applications.



Lectures on Ergodic Theory

Lectures on Ergodic Theory Author Paul Richard Halmos
ISBN-10 LCCN:a59000156
Release 1956
Pages 99
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Lectures on Ergodic Theory has been writing in one form or another for most of life. You can find so many inspiration from Lectures on Ergodic Theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Lectures on Ergodic Theory book for free.



Invitation to Ergodic Theory

Invitation to Ergodic Theory Author César Ernesto Silva
ISBN-10 9780821844205
Release 2008
Pages 262
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This book is an introduction to basic concepts in ergodic theory such as recurrence, ergodicity, the ergodic theorem, mixing, and weak mixing. It does not assume knowledge of measure theory; all the results needed from measure theory are presented from scratch. In particular, the book includes a detailed construction of the Lebesgue measure on the real line and an introduction to measure spaces up to the Caratheodory extension theorem. It also develops the Lebesgue theory of integration, including the dominated convergence theorem and an introduction to the Lebesgue $L^p$spaces. 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.



An Introduction to Ergodic Theory

An Introduction to Ergodic Theory Author Peter Walters
ISBN-10 0387951520
Release 2000-10-06
Pages 250
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This text provides an introduction to ergodic theory suitable for readers knowing basic measure theory. The mathematical prerequisites are summarized in Chapter 0. It is hoped the reader will be ready to tackle research papers after reading the book. The first part of the text is concerned with measure-preserving transformations of probability spaces; recurrence properties, mixing properties, the Birkhoff ergodic theorem, isomorphism and spectral isomorphism, and entropy theory are discussed. Some examples are described and are studied in detail when new properties are presented. The second part of the text focuses on the ergodic theory of continuous transformations of compact metrizable spaces. The family of invariant probability measures for such a transformation is studied and related to properties of the transformation such as topological traitivity, minimality, the size of the non-wandering set, and existence of periodic points. Topological entropy is introduced and related to measure-theoretic entropy. Topological pressure and equilibrium states are discussed, and a proof is given of the variational principle that relates pressure to measure-theoretic entropies. Several examples are studied in detail. The final chapter outlines significant results and some applications of ergodic theory to other branches of mathematics.



Ergodic Theory

Ergodic Theory Author Manfred Einsiedler
ISBN-10 0857290215
Release 2010-09-11
Pages 481
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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.



Dynamical Systems and Ergodic Theory

Dynamical Systems and Ergodic Theory Author Mark Pollicott
ISBN-10 0521575990
Release 1998-01-29
Pages 179
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This book is essentially a 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 master's 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).



Algebraic Ideas in Ergodic Theory

Algebraic Ideas in Ergodic Theory Author Klaus Schmidt
ISBN-10 0821889206
Release 1990
Pages 94
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Algebraic Ideas in Ergodic Theory has been writing in one form or another for most of life. You can find so many inspiration from Algebraic Ideas in Ergodic Theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Algebraic Ideas in Ergodic Theory book for free.



Topics in Ergodic Theory PMS 44

Topics in Ergodic Theory  PMS 44 Author Iakov Grigorevich Sinai
ISBN-10 9781400887255
Release 2017-03-14
Pages 226
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This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.



Lectures on Lyapunov Exponents

Lectures on Lyapunov Exponents Author Marcelo Viana
ISBN-10 9781316062692
Release 2014-07-24
Pages
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The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.



Ergodic Theory Groups and Geometry

Ergodic Theory  Groups  and Geometry Author Robert J. Zimmer
ISBN-10 9780821809808
Release 2008
Pages 87
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The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure-theoretic techniques. This book provides an introduction to some of the important methods, major developments, and open problems in the subject. It is slightly expanded from lectures given by Zimmer at the CBMS conference at the University of Minnesota. The main text presents a perspective on the field as it was at that time. Comments at the end of each chapter provide selected suggestions for further reading, including references to recent developments.



Lectures on Measure and Integration

Lectures on Measure and Integration Author Harold Widom
ISBN-10 9780486810287
Release 2016-11-16
Pages 176
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These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.



Foundations of Ergodic Theory

Foundations of Ergodic Theory Author Marcelo Viana
ISBN-10 9781107126961
Release 2016-02-12
Pages 625
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Self-contained introductory textbook suitable for a variety of one- or two-semester courses. Rich with examples, applications and exercises.



Lyapunov Exponents and Smooth Ergodic Theory

Lyapunov Exponents and Smooth Ergodic Theory Author Luis Barreira
ISBN-10 9780821829219
Release 2002-01
Pages 151
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This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). The authors consider several non-trivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory. This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field.



Recurrence in Ergodic Theory and Combinatorial Number Theory

Recurrence in Ergodic Theory and Combinatorial Number Theory Author Harry Furstenberg
ISBN-10 9781400855162
Release 2014-07-14
Pages 216
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Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.