# AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

# Small divisor problem in the theory of three-dimensional water gravity waves

### About this Title

**Gérard Iooss** and **Pavel I. Plotnikov**

Publication: Memoirs of the American Mathematical Society

Publication Year:
2009; Volume 200, Number 940

ISBNs: 978-0-8218-4382-6 (print); 978-1-4704-0554-0 (online)

DOI: https://doi.org/10.1090/memo/0940

MathSciNet review: 2529006

MSC: Primary 76B15; Secondary 35B32, 35S15, 37K55, 47G30, 47J15, 47N20, 76B07

### Table of Contents

**Chapters**

- Chapter 1. Introduction
- Chapter 2. Formal solutions
- Chapter 3. Linearized operator
- Chapter 4. Small divisors. Estimate of $\mathfrak {L}$-resolvent
- Chapter 5. Descent method-inversion of the linearized operator
- Chapter 6. Nonlinear problem. Proof of Theorem 1.3
- Appendix A. Analytical study of $G_n$
- Appendix B. Formal computation of 3-dimensional waves
- Appendix C. Proof of Lemma 3.6
- Appendix D. Proofs of lemmas 3.7 and 3.8
- Appendix E. Distribution of numbers $\{\omega _0 n^2\}$
- Appendix F. Pseudodifferential operators
- Appendix G. Dirichlet-Neumann operator
- Appendix H. Proof of Lemma 5.8
- Appendix I. Fluid particles dynamics