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Author: Karl Endel Petersen
Publisher: Cambridge University Press
Published: 1995
Total Pages: 452
ISBN-13: 0521459990
DOWNLOAD EBOOK →Tutorial survey papers on important areas of ergodic theory, with related research papers.
Author: Joseph Rosenblatt
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 242
ISBN-13: 0821842358
DOWNLOAD EBOOK →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.
Author: Karl Endel Petersen
Publisher:
Published: 2014-05-14
Total Pages: 450
ISBN-13: 9781107362048
DOWNLOAD EBOOK →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: Karl E. Petersen
Publisher:
Published: 1995
Total Pages: 448
ISBN-13: 9781107366954
DOWNLOAD EBOOK →Tutorial survey papers on important areas of ergodic theory, with related research papers.
Author: Alexander Gorodnik
Publisher: Princeton University Press
Published: 2010
Total Pages: 136
ISBN-13: 0691141851
DOWNLOAD EBOOK →The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established.
Author: Karl E. Petersen
Publisher: Cambridge University Press
Published: 1995-01-27
Total Pages: 0
ISBN-13: 9780521459990
DOWNLOAD EBOOK →This volume contains articles that describe the connections between ergodic theory and convergence, rigidity theory, and the theory of joinings. These papers present the background of each area of interaction, the most outstanding recent results, and the currently promising lines of research. In the aggregate, they will provide a perfect introduction for anyone beginning research in one of these areas.
Author: Idris Assani
Publisher: Walter de Gruyter
Published: 2013-12-12
Total Pages: 288
ISBN-13: 3110298201
DOWNLOAD EBOOK →This is the proceedings of the workshop on recent developments in ergodic theory and dynamical systems on March 2011 and March 2012 at the University of North Carolina at Chapel Hill. The articles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval exchange transformations, continued fractions, return times averages, Furstenberg Fractals, fractal geometry of non-uniformly hyperbolic horseshoes, convergence along the sequence of squares, adic and horocycle flows, and topological flows. These contributions illustrate the connections between ergodic theory and dynamical systems, number theory, harmonic analysis, probability, and algebra. Two surveys are included which give a nice introduction for interested young or senior researcher to some active research areas. Overall this volume provides a very useful blend of techniques and methods as well as directions of research on general convergence phenomena in ergodic theory and dynamical systems.
Author: Bernard Host
Publisher: American Mathematical Soc.
Published: 2018-12-12
Total Pages: 427
ISBN-13: 1470447800
DOWNLOAD EBOOK →Nilsystems play a key role in the structure theory of measure preserving systems, arising as the natural objects that describe the behavior of multiple ergodic averages. This book is a comprehensive treatment of their role in ergodic theory, covering development of the abstract theory leading to the structural statements, applications of these results, and connections to other fields. Starting with a summary of the relevant dynamical background, the book methodically develops the theory of cubic structures that give rise to nilpotent groups and reviews results on nilsystems and their properties that are scattered throughout the literature. These basic ingredients lay the groundwork for the ergodic structure theorems, and the book includes numerous formulations of these deep results, along with detailed proofs. The structure theorems have many applications, both in ergodic theory and in related fields; the book develops the connections to topological dynamics, combinatorics, and number theory, including an overview of the role of nilsystems in each of these areas. The final section is devoted to applications of the structure theory, covering numerous convergence and recurrence results. The book is aimed at graduate students and researchers in ergodic theory, along with those who work in the related areas of arithmetic combinatorics, harmonic analysis, and number theory.
