Translator Disclaimer
1997 Morse theory for trajectories of Lagrangian systems on Riemannian manifolds with convex boundary
Rossella Bartolo, Antonio Masiello
Adv. Differential Equations 2(4): 593-618 (1997).

Abstract

In this paper we relate the set of the orbits of a second-order Lagrangian systems joining two points on an open set with convex boundary of a Riemannian manifold with the topological structure of the open set. Such relations are obtained by developing a Morse Theory for the action integral of the Lagrangian system. Because of the presence of the boundary, the action integral does not satisfy the Palais-Smale condition. We perturb the action integral with a family of smooth functionals, satisfying the Palais-Smale condition. The Morse Relations for the action integral are obtained as limit of the Morse Relations of the perturbing functionals. A relation between the Morse index and the energy of the orbits as critical points of the action integral is obtained.

Citation

Download Citation

Rossella Bartolo. Antonio Masiello. "Morse theory for trajectories of Lagrangian systems on Riemannian manifolds with convex boundary." Adv. Differential Equations 2 (4) 593 - 618, 1997.

Information

Published: 1997
First available in Project Euclid: 23 April 2013

zbMATH: 1023.58500
MathSciNet: MR1441858

Subjects:
Primary: 58E10
Secondary: 34B15, 58E05, 70H35

Rights: Copyright © 1997 Khayyam Publishing, Inc.

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.2 • No. 4 • 1997
Back to Top