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· 제목 : Nilpotent Structures in Ergodic Theory (Hardcover)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470447809
· 쪽수 : 427쪽
· 출판일 : 2019-01-14
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470447809
· 쪽수 : 427쪽
· 출판일 : 2019-01-14
목차
- 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 $\ell^\infty$ and pointwise convergence of cubic averages
- Multiple correlations, good weights, and anti-uniformity
- Inverse results for uniformity seminorms and applications
- The comparison method
- Bibliography
- Index of terms
- Index of symbols.
