Nilpotent Structures in Ergodic Theory (Hardcover)

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.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Mathematical Surveys and Monographs
Release date:	2019
Authors:	Bernard Host • Bryna Kra
Dimensions:	254 x 178mm (L x W)
Format:	Hardcover
Pages:	427
ISBN-13:	978-1-4704-4780-9
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > General Promotions
LSN:	1-4704-4780-0
Barcode:	9781470447809

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