Nilpotent Structures in Ergodic Theory is popular PDF and ePub book, written by Bernard Host in 2018-12-12, it is a fantastic choice for those who relish reading online the Ergodic theory genre. Let's immerse ourselves in this engaging Ergodic theory book by exploring the summary and details provided below. Remember, Nilpotent Structures in Ergodic Theory can be Read Online from any device for your convenience.
Nilpotent Structures in Ergodic Theory Book PDF Summary
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.
Detail Book of Nilpotent Structures in Ergodic Theory PDF
- Author : Bernard Host
- Release : 12 December 2018
- Publisher : American Mathematical Soc.
- ISBN : 9781470447809
- Genre : Ergodic theory
- Total Page : 427 pages
- Language : English
- PDF File Size : 10,9 Mb
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