The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
type: Item
instance of: scholarly article
title: The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
zbMATH Open document ID: 1200.53072
DOI: 10.1134/S0001434610030168
author: Sergei Yu. Dobrokhotov
author: Michel Rouleux
published in: Mathematical Notes
publication date: 2010-09-24T00:00:00Z
review text: The authors of this paper intend to show that one can obtain certain spectral series if the Hamiltonian system possesses only one (individual) invariant Lagrangian torus with almost periodic or periodic motion and explain how one can obtain such tori using the Maupertuis-Jacobi correspondence. In this respect, the authors have shown that the existence of almost invariant Lagrangian tori follows from the Darboux-Weinstein theorem for general Lagrangian manifolds, and they give a simpler proof and sufficiently explicit formulas in the case considered. The present theory is applied to water wave theory by observing that a Hamiltonian operator \(\chi (x,p ) = g(x) p^2\) is determined by a Liouville metric \(g (x)\) in a plane domain \(\Omega\) diffeomorphic to an annulus.
Mathematics Subject Classification ID: 53D12
zbMATH DE Number: 5791067
zbMATH Keywords: Maslov canonical operator
zbMATH Keywords: complete integrability
zbMATH Keywords: Liouville tori
zbMATH Keywords: KAM tori
zbMATH Keywords: Maupertuis-Jacobi correspondence
reviewed by: Ioan Pop
MaRDI profile type: Publication
cites work: Q3896271
cites work: Q4397699
cites work: Quasi-modes sur les variétés Riemanniennes
cites work: Lectures on the geometry of quantization
cites work: Q4174811
cites work: The Maupertuis Principle and Canonical Transformations of the Extended Phase Space
cites work: Q3311232
full work available at URL: s0001434610030168
OpenAlex ID: W1966204369
description: scientific article; zbMATH DE number 5791067