The inverse function theorem of Nash and Moser

Hamilton, Richard S.

doi:10.1090/s0273-0979-1982-15004-2

Cited by 975 publications

(1,226 citation statements)

References 17 publications

Supporting

Mentioning

1,178

Contrasting

Unclassified

Order By: Relevance

“…The next lemma is also classical, see for example [26], Appendix, and [27], Appendix G. The present version is proved in [2], adapting Lemma 2.3.6 on page 149 of [25], except for the part on the Lipschitz dependence on a parameter, which is proved here below.…”

Section: Lemma 63 (Lipschitz Estimate On Parameters)mentioning

confidence: 82%

See 1 more Smart Citation

KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation

2014

View full text Add to dashboard Cite

Abstract:We prove the existence of quasi-periodic, small amplitude, solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities we also obtain the linear stability of the solutions. The proofs are based on a combination of different ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a differential operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coefficients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues.

show abstract

Section: Lemma 63 (Lipschitz Estimate On Parameters)mentioning

confidence: 82%

“…Now consider a transformation of type (b), namely a change of the time variable 25) where α = α(ϕ), ϕ ∈ T ν , is a 2π-periodic function of ν variables (in other words, t → t + α(ωt) is the diffeomorphisms of R induced by the transformation B). If u(t) is a solution of (2.21), then v(τ ), defined by u = Bv, solves…”

Section: Dynamical Reducibilitymentioning

confidence: 99%

KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation

2014

View full text Add to dashboard Cite

show abstract

“…By a marking of a Fréchet space E we shall understand an increasing family (p n ) n∈N of semi-norms which define the topology on E. Pairs (E, (p n ) n ) will henceforth be called marked Fréchet spaces -in the literature one also finds the notion of graded Fréchet space (see [9]). …”

Section: Discussionmentioning

confidence: 99%

Smooth Fréchet globalizations of Harish-Chandra modules

2013

View full text Add to dashboard Cite

“…Le lecteur pourra se reporter a [Ham82] pour les outils fondamentaux, ou a [Lab89] ou la meme mecanique est utilisee dans un cas similaire.…”

Section: Analyseunclassified

Surfaces convexes dans des espaces lorentziens à courbure constante

Schlenker¹

1996

Communications in Analysis and Geometry

View full text Add to dashboard Cite

ResumeNous etudions les immersions isometriques de surfaces a courbure K < KQ dans des espaces lorentziens de dimension 3 a courbure constante, et en particulier les degenerescences de suites de telles immersions. Nous en deduisons des resultats d'existence et d'unicite d'immersions isometriques de surfaces compactes dans I'espace de Sitter, ainsi que des resultats d'existence quand les surfaces sont seulement completes. AbstractWe study isometric immersions of surfaces with curvature K < KQ in 3-dimensionnal Lorentz spaces with constant curvature KQ, and more specifically degeneracies of sequences of such immersions. Then we use those results to prove existence and unicity for some isometric immersions of compact surfaces in the de Sitter space, as well as existence results for complete surfaces.

show abstract

The inverse function theorem of Nash and Moser

Cited by 975 publications

References 17 publications

KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation

KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation

Smooth Fréchet globalizations of Harish-Chandra modules

Surfaces convexes dans des espaces lorentziens à courbure constante

Contact Info

Product

Resources

About