On the Lebesgue measure of the periodic points of a contact manifold
type: Item
instance of: scholarly article
title: On the Lebesgue measure of the periodic points of a contact manifold
zbMATH Open document ID: 0816.58008
DOI: 10.1007/BF02571890
author: Vesselin Petkov
author: Georgi Popov
published in: Mathematische Zeitschrift
publication date: 1995-07-16T00:00:00Z
full work available at URL: https://eudml.org/doc/174715
review text: 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.
Mathematics Subject Classification ID: 58C35
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 737162
zbMATH Keywords: Lebesgue measure
zbMATH Keywords: periodic points
zbMATH Keywords: contact manifolds
MaRDI profile type: Publication
cites work: A semi-classical trace formula for Schrödinger operators
cites work: On the period spectrum of a symplectic mapping
cites work: Q4008513
cites work: Ergodicité et limite semi-classique. (Ergodicity and semi-classical limit)
cites work: Proprietes asymptotiques du spectre dioperateurs pseuwdifferentiels sur IRn
cites work: Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles
cites work: Q3736112
cites work: Asymptotique semi-classique du spectre d'hamiltoniens quantiques et trajectories classiques périodiques
cites work: Length spectrum invariants of Riemannian manifolds
cites work: A proof of Weinstein's conjecture in \(\mathbb R^{2n}\)
OpenAlex ID: W2091130411
description: scientific article; zbMATH DE number 737162