A smooth pseudo-gradient for the Lagrangian action functional by

  title={A smooth pseudo-gradient for the Lagrangian action functional by},
  author={Alberto Abbondandolo},
We study the action functional associated to a smooth Lagrangian function on the cotangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action functional is in general not twice differentiable on the Hilbert manifold consisting of H curves, it is a Lyapunov function for some smooth Morse-Smale vector field, under the generic assumption that all the critical points are non-degenerate. This fact is sufficient to associate a Morse complex to the… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 19 references

Periodic solutions of Lagrangian systems on a compact manifold

V. Benci
J. Diff. Eq., 63:135–161 • 1986
View 5 Excerpts
Highly Influenced

Lectures on the Morse complex for infinite dimensional manifolds

A. Abbondandolo, P. Majer
P. Biran, O. Cornea, and F. Lalonde, editors, Morse theoretic methods in nonlinear analysis and in symplectic topology, pages 1–74, Montreal • 2006
View 3 Excerpts
Highly Influenced

Splitting theorem

C. Li, S. Li, J. Liu
Poincaré-Hopf theorem and jumping nonlinear problems. J. Funct. Anal., 221(2):439–455 • 2005
View 1 Excerpt

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