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Nilpotent structures in ergodic theory /

Bibliographic Details
Main Authors: Host, B. (Bernard) (Author), Kra, Bryna, 1966- (Author)
Format: Book
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2018]
Series:Mathematical surveys and monographs ; no. 236.
Subjects:
Ergodic theory.
Nilpotent groups.
Isomorphisms (Mathematics)
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 anti-uniformity
  • Inverse results for uniformity seminorms and applications
  • The comparison method.