On the Lebesgue measure of the periodic points of a contact manifold
This paper is concerned with the Lebesgue measure of the periodic points of contact vector fields on contact manifolds. For any smooth contact manifold we prove that the Lebesgue measure of the set of the periodic points is equal to that of the absolutely periodic points. As a consequence we obtain that for any analytic connected and complete contact manifold either the Lebesgue measure of the periodic points is zero or the flow of the corresponding vector field is totally periodic. A similar result is proved for the periodic points of a Hamiltonian vector field on an energy surface of a contact type. Applications in the semi- classical asymptotics of the Schrödinger operator are obtained.
scientific article; zbMATH DE number 737162