Nilpotent structures in ergodic theory / Bernard Host, Bryna Kra.
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Main Authors:  , 

Format:  Book 
Language:  English 
Published: 
Providence, Rhode Island :
American Mathematical Society,
[2018]

Series:  Mathematical surveys and monographs ;
no. 236. 
Subjects: 
Dynamical systems and ergodic theory
> Ergodic theory
> Ergodic theorems, spectral theory, Markov operators.
Dynamical systems and ergodic theory
> Ergodic theory
> Relations with number theory and harmonic analysis.

Table of Contents:
 Introduction
 Part 1. Basics. Background material
 Dynamical background
 Rotations
 Group extensions
 Part 2. Cubes. Cubes in an algebraic setting
 Dynamical cubes
 Cubes in ergodic theory
 The structure factors
 Part 3. Nilmanifolds and nilsystems. Nilmanifolds
 Nilsystems
 Cubic structures in nilmanifolds
 Factors of nilsystems
 Polynomials in nilmanifolds and nilsystems
 Arithmetic progressions in nilsystems
 Part 4. Structure theorems. The ergodic structure theorem
 Other structure theorems
 Relations between consecutive factors
 The structure theorem in a particular case
 The structure theorem in the general case
 Part 5. Applications. The method of characteristic factors
 Uniformity seminorms on ℓ[infinity]
 Multiple correlations, good weights, and antiuniformity
 Inverse results for uniformity seminorms and applications
 The comparison method.