Quasi-Periodic Solutions of Nonlinear Wave Equations on the dd-Dimensional Torus

  • Massimiliano Berti

    SISSA, Trieste, Italy
  • Philippe Bolle

    Avignon Université, France
Quasi-Periodic Solutions of Nonlinear Wave Equations on the d-Dimensional Torus cover
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FrontmatterDownload pp. i–iv
PrefaceDownload pp. v–xi
ContentsDownload pp. xiii–xv
1IntroductionDownload pp. 1–18
2KAM for PDEs and strategy of proofpp. 19–68
3Hamiltonian formulationpp. 69–76
4Functional settingpp. 77–111
5Multiscale Analysispp. 113–164
6Nash–Moser theorempp. 165–174
7Linearized operator at an approximate solutionpp. 175–188
8Splitting of low-high normal subspaces up to O(ϵ4)O(\epsilon^4)pp. 189–198
9Approximate right inverse in normal directionspp. 199–203
10Splitting between low-high normal subspacespp. 205–245
11Construction of approximate right inversepp. 247–270
12Proof of the Nash–Moser Theorempp. 271–294
13Genericity of the assumptionspp. 295–310
AHamiltonian and reversible PDEspp. 311–318
BMultiscale Steppp. 319–336
CNormal form close to an isotropic toruspp. 337–348
Bibliographypp. 349–355
Indexpp. 357–358