A semiclassical Birkhoff normal form for symplectic magnetic wells

Spectral asymptotics via the semiclassical Birkhoff normal form

This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy E. This permits a detailed study of the spectrum in various asymptotic regions of the parameters (E...

BIRKHOFF NORMAL FORM FOR SOME NONLINEAR PDEs

. SP ] 3 M ay 2 00 6 Spectral asymptotics via the semiclassical Birkhoff normal form

This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy E. This permits a detailed study of the spectrum in various asymptotic regions of the parameters (E...

A Program to Compute Birkhoff Normal Formsof Symplectic Maps In

A program to compute the Birkhoo normal forms for symplectic maps in l R 4 is described. We consider the case of an elliptic xed point, which is the most relevant for applications. We compute the normal forms both in the nonresonant and resonant case and we provide the interpolating hamiltonian and the normalizing transformation. Programming language: Fortran 77. High speed storage required: 1....

Birkhoff Normal Form and Hamiltonian PDEs

These notes are based on lectures held at the Lanzhou university (China) during a CIMPA summer school in july 2004 but benefit from recent devellopements. Our aim is to explain some perturbations technics that allow to study the long time behaviour of the solutions of Hamiltonian perturbations of integrable systems. We are in particular interested with stability results. Our approach is centere...