Recurrence In Ergodic Theory And Combinatorial Number Theory

Author : Harry Furstenberg
Publisher : Princeton University Press
Page : 216 pages
File Size : 45,9 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400855162

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Recurrence in Ergodic Theory and Combinatorial Number Theory by Harry Furstenberg Pdf

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 : Manfred Einsiedler,Thomas Ward
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 41,8 Mb
Release : 2010-09-11
Category : Mathematics
ISBN : 9780857290212

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Ergodic Theory by Manfred Einsiedler,Thomas Ward Pdf

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 : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 42,9 Mb
Release : 2018-06-15
Category : Mathematics
ISBN : 9783319749082

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk Pdf

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.

Author : Marcelo Viana,Krerley Oliveira
Publisher : Cambridge University Press
Page : 547 pages
File Size : 41,8 Mb
Release : 2016-02-15
Category : Mathematics
ISBN : 9781107126961

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Foundations of Ergodic Theory by Marcelo Viana,Krerley Oliveira Pdf

Self-contained introductory textbook suitable for a variety of one- or two-semester courses. Rich with examples, applications and exercises.

Author : Melvyn B. Nathanson
Publisher : Springer
Page : 312 pages
File Size : 47,9 Mb
Release : 2014-10-18
Category : Mathematics
ISBN : 9781493916016

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Combinatorial and Additive Number Theory by Melvyn B. Nathanson Pdf

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.

Author : Sukumar Das Adhikari
Publisher : Unknown
Page : 184 pages
File Size : 52,7 Mb
Release : 2002
Category : Combinatorial analysis
ISBN : 8173193037

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Aspects of Combinatorics and Combinatorial Number Theory by Sukumar Das Adhikari Pdf

Author : Vitaly Bergelson,Peter March,Joseph Rosenblatt
Publisher : Walter de Gruyter
Page : 461 pages
File Size : 40,8 Mb
Release : 2011-06-15
Category : Mathematics
ISBN : 9783110889383

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Convergence in Ergodic Theory and Probability by Vitaly Bergelson,Peter March,Joseph Rosenblatt Pdf

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.

Author : Cesar E. Silva,Alexandre I. Danilenko
Publisher : Springer Nature
Page : 707 pages
File Size : 42,9 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781071623886

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Ergodic Theory by Cesar E. Silva,Alexandre I. Danilenko Pdf

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

Author : Mark Pollicott,Michiko Yuri
Publisher : Cambridge University Press
Page : 198 pages
File Size : 50,9 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521575990

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Dynamical Systems and Ergodic Theory by Mark Pollicott,Michiko Yuri Pdf

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).

Author : Karl E. Petersen
Publisher : Cambridge University Press
Page : 452 pages
File Size : 45,9 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 9780521459990

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Ergodic Theory and Harmonic Analysis by Karl E. Petersen Pdf

Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics.

Author : Mark Pollicott,Klaus Schmidt
Publisher : Cambridge University Press
Page : 496 pages
File Size : 51,7 Mb
Release : 1996-03-28
Category : Mathematics
ISBN : 9780521576888

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Ergodic Theory and Zd Actions by Mark Pollicott,Klaus Schmidt Pdf

A mixture of surveys and original articles that span the theory of Zd actions.

Author : Karl E. Petersen,Karl Petersen
Publisher : Cambridge University Press
Page : 348 pages
File Size : 48,8 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.

Author : Peter Walters
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 48,9 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.

Author : Ethan Akin
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 49,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475726688

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Recurrence in Topological Dynamics by Ethan Akin Pdf

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.

Author : Weltausstellung (1862, London)
Publisher : Unknown
Page : 134 pages
File Size : 53,6 Mb
Release : 1862
Category : Electronic
ISBN : DMM:057002288789-150810

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Official Illustrated Catalogue by Weltausstellung (1862, London) Pdf