Michel VITTOT (Centre de Physique Theorique, CNRS Luminy, Marseille, France)
Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula
(69K, latex2e)
ABSTRACT. We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the algebra of observables. We give a bound for the perturbation in order to solve this inversion. And apply this result to a particular case of the control theory, as a first example, and to the ``quantum adiabatic transformation'', as another example.