Nil Bohr-sets and almost automorphy of higher order
Two closely related topics: higher order Bohr sets and higher order almost automorphy are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any In...
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| Hlavní autoři: | , , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Providence, Rhode Island
American Mathematical Society
2016
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| Vydání: | 1 |
| Edice: | Memoirs of the American Mathematical Society |
| Témata: | |
| ISBN: | 9781470418724, 147041872X |
| ISSN: | 0065-9266, 1947-6221 |
| On-line přístup: | Získat plný text |
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- Introduction -- Preliminaries -- Nilsystems -- Generalized polynomials -- Nil Bohr<inline-formula content-type="math/mathml"> 0 _0 </inline-formula>-sets and generalized polynomials: Proof of Theorem B -- Generalized polynomials and recurrence sets: Proof of Theorem C -- Recurrence sets and regionally proximal relation of order <inline-formula content-type="math/mathml"> d d </inline-formula> -- <inline-formula content-type="math/mathml"> d d </inline-formula>-step almost automorpy and recurrence sets
- Cover -- Title page -- Chapter 1. Introduction -- 1.1. Higher order Bohr problem -- 1.2. Higher order almost automorphy -- 1.3. Further questions -- 1.4. Organization of the paper -- Chapter 2. Preliminaries -- 2.1. Basic notions -- 2.2. Bergelson-Host-Kra' Theorem and the proof of Theorem A(2) -- 2.3. Equivalence of Problems B-I,II,III -- Chapter 3. Nilsystems -- 3.1. Nilmanifolds and nilsystems -- 3.2. Nilpotent Matrix Lie Group -- Chapter 4. Generalized polynomials -- 4.1. Definitions -- 4.2. Basic properties of generalized polynomials -- Chapter 5. Nil Bohr₀-sets and generalized polynomials: Proof of Theorem B -- 5.1. Proof of Theorem B(1) -- 5.2. Proof of Theorem B(2) -- Chapter 6. Generalized polynomials and recurrence sets: Proof of Theorem C -- 6.1. A special case and preparation -- 6.2. Proof of Theorem C -- Chapter 7. Recurrence sets and regionally proximal relation of order -- 7.1. Regionally proximal relation of order -- 7.2. Nil_{ } Bohr₀-sets, Poincaré sets and \RP^{[ ]} -- 7.3. _{ }-sets and \RP^{[ ]} -- 7.4. Cubic version of multiple recurrence sets and \RP^{[ ]} -- 7.5. Conclusion -- Chapter 8. -step almost automorpy and recurrence sets -- 8.1. Definition of -step almost automorpy -- 8.2. Characterization of -step almost automorphy -- Appendix A. -- A.1. The Ramsey properties -- A.2. Compact Hausdorff systems -- A.3. Intersective -- Bibliography -- Index -- Back Cover