
eBook ISBN: | 978-1-4704-0286-0 |
Product Code: | MEMO/146/695.E |
List Price: | $52.00 |
MAA Member Price: | $46.80 |
AMS Member Price: | $31.20 |

eBook ISBN: | 978-1-4704-0286-0 |
Product Code: | MEMO/146/695.E |
List Price: | $52.00 |
MAA Member Price: | $46.80 |
AMS Member Price: | $31.20 |
-
Book DetailsMemoirs of the American Mathematical SocietyVolume: 146; 2000; 106 ppMSC: Primary 28; Secondary 05; 11
We prove a polynomial multiple recurrence theorem for finitely many commuting measure preserving transformations of a probability space, extending a polynomial Szemerédi theorem appearing in [BL1]. The linear case is a consequence of an ergodic IP-Szemerédi theorem of Furstenberg and Katznelson ([FK2]). Several applications to the fine structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which we also prove a multiparameter weakly mixing polynomial ergodic theorem. The techniques and apparatus employed include a polynomialization of an IP structure theory developed in [FK2], an extension of Hindman's theorem due to Milliken and Taylor ([M], [T]), a polynomial version of the Hales-Jewett coloring theorem ([BL2]), and a theorem concerning limits of polynomially generated IP-systems of unitary operators ([BFM]).
ReadershipResearchers interested in measure-preserving transformations, partitions of integers, Ramsey theory, sequences and sets.
-
Table of Contents
-
Chapters
-
0. Introduction
-
1. Formulation of main theorem
-
2. Preliminaries
-
3. Primitive extensions
-
4. Relative polynomial mixing
-
5. Completion of the proof
-
6. Measure-theoretic applications
-
7. Combinatorial applications
-
8. For future investigation
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
We prove a polynomial multiple recurrence theorem for finitely many commuting measure preserving transformations of a probability space, extending a polynomial Szemerédi theorem appearing in [BL1]. The linear case is a consequence of an ergodic IP-Szemerédi theorem of Furstenberg and Katznelson ([FK2]). Several applications to the fine structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which we also prove a multiparameter weakly mixing polynomial ergodic theorem. The techniques and apparatus employed include a polynomialization of an IP structure theory developed in [FK2], an extension of Hindman's theorem due to Milliken and Taylor ([M], [T]), a polynomial version of the Hales-Jewett coloring theorem ([BL2]), and a theorem concerning limits of polynomially generated IP-systems of unitary operators ([BFM]).
Researchers interested in measure-preserving transformations, partitions of integers, Ramsey theory, sequences and sets.
-
Chapters
-
0. Introduction
-
1. Formulation of main theorem
-
2. Preliminaries
-
3. Primitive extensions
-
4. Relative polynomial mixing
-
5. Completion of the proof
-
6. Measure-theoretic applications
-
7. Combinatorial applications
-
8. For future investigation