Lectures on Ergodic Theory PDF Download
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Author: Paul R. Halmos
Publisher: Courier Dover Publications
ISBN: 0486826848
Category : Mathematics
Languages : en
Pages : 113
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Book Description
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: Paul R. Halmos
Publisher: Courier Dover Publications
ISBN: 0486826848
Category : Mathematics
Languages : en
Pages : 113
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Book Description
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: 9780521435932
Category : Mathematics
Languages : en
Pages : 176
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Book Description
These lecture notes provide a unique introduction to Pesin theory and its applications.
Author: P. Walters
Publisher: Springer
ISBN: 3540374949
Category : Mathematics
Languages : en
Pages : 209
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Book Description
Author: Manfred Einsiedler
Publisher: Springer Science & Business Media
ISBN: 0857290215
Category : Mathematics
Languages : en
Pages : 486
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Book Description
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: Harry Furstenberg
Publisher: Princeton University Press
ISBN: 1400855160
Category : Mathematics
Languages : en
Pages : 216
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Book Description
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.
Author: Karma Dajani
Publisher: CRC Press
ISBN: 1000402770
Category : Mathematics
Languages : en
Pages : 268
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Book Description
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: Peter Walters
Publisher: Springer Science & Business Media
ISBN: 9780387951522
Category : Mathematics
Languages : en
Pages : 268
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Book Description
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: Karl E. Petersen
Publisher: Cambridge University Press
ISBN: 9780521389976
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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.
Author: Paul Richard Halmos
Publisher: Chelsea Publishing Company, Incorporated
ISBN: 9780828401425
Category : Ergodic theory
Languages : en
Pages : 99
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Book Description
Author: Robert Edward Bowen
Publisher: Springer
ISBN: 3540776958
Category : Mathematics
Languages : en
Pages : 85
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Book Description
For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."
