The Palais-Smale condition on contact type energy levels for convex Lagrangian systems

By G. Contreras. 2003

85 citations recorded by the source corpus.

We prove that for a uniformly convex Lagrangian system L on a compact manifold M, almost all energy levels contain a periodic orbit. We also prove that below Mañé's critical value of the lift of the Lagrangian to the universal cover, cu(L), almost all energy levels have conjugate points.We in addition prove that if an energy level is of contact type, projects onto M and $$M\ne{\mathbb T}^2$$, then the free time action functional of L+k satisfies the Palais-Smale condition.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/078cffe9f772a54d2d67d98c3fff9a5bcc5e76d6

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In Applied Mathematics

1. Basak Z. Gurel
2. V. Ginzburg
3. Michael Usher

In Computational Theory and Mathematics

1. Basak Z. Gurel
2. V. Ginzburg

Citations in the corpus

• Periodic Orbits of Twisted Geodesic Flows and The Weinstein-Moser Theorem (2007, background): “, [No], [NT], [Ta1], [Ta2] in the context of Morse–Novikov theory; see also [Co], [CIPP], [CMP], [Gi6] for further references.”