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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)
MathSciNet review: 2529006
MSC: Primary 76B15; Secondary 35B32, 35S15, 37K55, 47G30, 47J15, 47N20, 76B07

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Table of Contents


  • 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