KAM theory in momentum space and quasiperiodic Schrödinger operators
KAM Tori and Quantum Birkhoff Normal Forms
This talk is concerned with the Kolmogorov-Arnold-Moser (KAM) theorem in Gevrey classes for analytic hamiltonians, the effective stability around the corresponding KAM tori, and the semi-classical asymptotics for Schrödinger operators with exponentially small error terms. Given a real analytic Hamiltonian close to a completely integrable one and a suitable Cantor set defined by a Diophantine condition, we find a family , of KAM invariant tori of with frequencies which is Gevrey smooth with...
Kreǐn's trace formula and the spectral shift function.