Recurrence In Ergodic Theory And Combinatorial Number Theory

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Recurrence in Ergodic Theory and Combinatorial Number Theory

Author : Harry Furstenberg
Publisher : Princeton University Press
ISBN 13 : 1400855160
Total Pages : 216 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Recurrence in Ergodic Theory and Combinatorial Number Theory by : Harry Furstenberg

Download or read book Recurrence in Ergodic Theory and Combinatorial Number Theory written by Harry Furstenberg and published by Princeton University Press. This book was released on 2014-07-14 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ergodic Theory

Author : Manfred Einsiedler
Publisher : Springer Science & Business Media
ISBN 13 : 0857290215
Total Pages : 486 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Ergodic Theory by : Manfred Einsiedler

Download or read book Ergodic Theory written by Manfred Einsiedler and published by Springer Science & Business Media. This book was released on 2010-09-11 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

Author : Sébastien Ferenczi
Publisher : Springer
ISBN 13 : 3319749080
Total Pages : 434 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by : Sébastien Ferenczi

Download or read book Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics written by Sébastien Ferenczi and published by Springer. This book was released on 2018-06-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Combinatorial and Additive Number Theory

Author : Melvyn B. Nathanson
Publisher : Springer
ISBN 13 : 1493916017
Total Pages : 309 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Combinatorial and Additive Number Theory by : Melvyn B. Nathanson

Download or read book Combinatorial and Additive Number Theory written by Melvyn B. Nathanson and published by Springer. This book was released on 2014-10-18 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems and future challenges in number theory.

Aspects of Combinatorics and Combinatorial Number Theory

Author : Sukumar Das Adhikari
Publisher :
ISBN 13 : 9788173193033
Total Pages : 184 pages
Book Rating : 4.1/5 (93 download)

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Book Synopsis Aspects of Combinatorics and Combinatorial Number Theory by : Sukumar Das Adhikari

Download or read book Aspects of Combinatorics and Combinatorial Number Theory written by Sukumar Das Adhikari and published by . This book was released on 2002 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Convergence in Ergodic Theory and Probability

Author : Vitaly Bergelson
Publisher : Walter de Gruyter
ISBN 13 : 3110889382
Total Pages : 461 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Convergence in Ergodic Theory and Probability by : Vitaly Bergelson

Download or read book Convergence in Ergodic Theory and Probability written by Vitaly Bergelson and published by Walter de Gruyter. This book was released on 2011-06-15 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.

Ergodic Theory

Author : Cesar E. Silva
Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva and published by Springer Nature. This book was released on 2023-07-31 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Mathematics of Ramsey Theory

Author : Jaroslav Nesetril
Publisher : Springer Science & Business Media
ISBN 13 : 3642729053
Total Pages : 279 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Mathematics of Ramsey Theory by : Jaroslav Nesetril

Download or read book Mathematics of Ramsey Theory written by Jaroslav Nesetril and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and survey articles by leading specialists. It surveys recent activity in this diverse subject and brings the reader up to the boundary of present knowledge. It covers virtually all main approaches to the subject and suggests various problems for individual research.

Dynamical Systems and Ergodic Theory

Author : Mark Pollicott
Publisher : Cambridge University Press
ISBN 13 : 9780521575997
Total Pages : 198 pages
Book Rating : 4.5/5 (759 download)

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Book Synopsis Dynamical Systems and Ergodic Theory by : Mark Pollicott

Download or read book Dynamical Systems and Ergodic Theory written by Mark Pollicott and published by Cambridge University Press. This book was released on 1998-01-29 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an essentially 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 masters 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).

Ergodic Theory and Its Connection with Harmonic Analysis

Author : Karl Endel Petersen
Publisher : Cambridge University Press
ISBN 13 : 0521459990
Total Pages : 452 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Ergodic Theory and Its Connection with Harmonic Analysis by : Karl Endel Petersen

Download or read book Ergodic Theory and Its Connection with Harmonic Analysis written by Karl Endel Petersen and published by Cambridge University Press. This book was released on 1995 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tutorial survey papers on important areas of ergodic theory, with related research papers.

Ergodic Theory and Zd Actions

Author : Mark Pollicott
Publisher : Cambridge University Press
ISBN 13 : 0521576881
Total Pages : 496 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Ergodic Theory and Zd Actions by : Mark Pollicott

Download or read book Ergodic Theory and Zd Actions written by Mark Pollicott and published by Cambridge University Press. This book was released on 1996-03-28 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mixture of surveys and original articles that span the theory of Zd actions.

Ergodic Theory

Author : Karl E. Petersen
Publisher : Cambridge University Press
ISBN 13 : 9780521389976
Total Pages : 348 pages
Book Rating : 4.3/5 (899 download)

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Book Synopsis Ergodic Theory by : Karl E. Petersen

Download or read book Ergodic Theory written by Karl E. Petersen and published by Cambridge University Press. This book was released on 1989-11-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Ergodic Theory

Author : Peter Walters
Publisher : Springer Science & Business Media
ISBN 13 : 9780387951522
Total Pages : 268 pages
Book Rating : 4.9/5 (515 download)

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Book Synopsis An Introduction to Ergodic Theory by : Peter Walters

Download or read book An Introduction to Ergodic Theory written by Peter Walters and published by Springer Science & Business Media. This book was released on 2000-10-06 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Recurrence in Topological Dynamics

Author : Ethan Akin
Publisher : Springer Science & Business Media
ISBN 13 : 1475726686
Total Pages : 271 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Recurrence in Topological Dynamics by : Ethan Akin

Download or read book Recurrence in Topological Dynamics written by Ethan Akin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the long run of a dynamical system, after transient phenomena have passed away, what remains is recurrence. An orbit is recurrent when it returns repeatedly to each neighborhood of its initial position. We can sharpen the concept by insisting that the returns occur with at least some prescribed frequency. For example, an orbit lies in some minimal subset if and only if it returns almost periodically to each neighborhood of the initial point. That is, each return time set is a so-called syndetic subset ofT= the positive reals (continuous time system) or T = the positive integers (discrete time system). This is a prototype for many of the results in this book. In particular, frequency is measured by membership in a family of subsets of the space modeling time, in this case the family of syndetic subsets of T. In applying dynamics to combinatorial number theory, Furstenberg introduced a large number of such families. Our first task is to describe explicitly the calculus of families implicit in Furstenberg's original work and in the results which have proliferated since. There are general constructions on families, e. g. , the dual of a family and the product of families. Other natural constructions arise from a topology or group action on the underlying set. The foundations are laid, in perhaps tedious detail, in Chapter 2. The family machinery is then applied in Chapters 3 and 4 to describe family versions of recurrence, topological transitivity, distality and rigidity.

Ergodic Theory via Joinings

Author : Eli Glasner
Publisher : American Mathematical Soc.
ISBN 13 : 1470419513
Total Pages : 384 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ergodic Theory via Joinings by : Eli Glasner

Download or read book Ergodic Theory via Joinings written by Eli Glasner and published by American Mathematical Soc.. This book was released on 2015-01-09 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Basic ergodic theory

Author : M. G. Nadkarni
Publisher : Springer
ISBN 13 : 9386279533
Total Pages : 200 pages
Book Rating : 4.3/5 (862 download)

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Book Synopsis Basic ergodic theory by : M. G. Nadkarni

Download or read book Basic ergodic theory written by M. G. Nadkarni and published by Springer. This book was released on 2013-01-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on Ergodic Theory. The presentation has a slow pace and the book can be read by any person with a background in basic measure theory and metric topology. A new feature of the book is that the basic topics of Ergodic Theory such as the Poincare 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 around the Glimm-Effros theorem are discussed. In the third edition a chapter entitled 'Additional Topics' has been added. It gives Liouville's Theorem on the existence of invariant measure, entropy theory leading up to Kolmogorov-Sinai Theorem, and the topological dynamics proof of van der Waerden's theorem on arithmetical progressions.

Logic and Combinatorics

Author : Stephen George Simpson
Publisher : American Mathematical Soc.
ISBN 13 : 0821850520
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Logic and Combinatorics by : Stephen George Simpson

Download or read book Logic and Combinatorics written by Stephen George Simpson and published by American Mathematical Soc.. This book was released on 1987 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, there was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level.