On the existence of homoclinic orbits on Riemannian manifolds
- 1 March 1994
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 14 (1) , 103-127
- https://doi.org/10.1017/s0143385700007744
Abstract
We prove the existence of a non-trivial homoclinic orbit on a Riemannian manifold (possibly non-compact), for Hamiltonian systems of the second order of the form: where the potential V is T-periodic in the time variable.Keywords
This publication has 16 references indexed in Scilit:
- On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systemsNonlinear Differential Equations and Applications NoDEA, 1994
- Homoclinic orbits in a first order superquadratic hamiltonian system: Convergence of subharmonic orbitsJournal of Differential Equations, 1991
- Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentialsJournal of the American Mathematical Society, 1991
- Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic PotentialsJournal of the American Mathematical Society, 1991
- Homoclinic orbits on compact manifoldsJournal of Mathematical Analysis and Applications, 1991
- Some quasilinear parabolic equationsNonlinear Analysis, 1991
- Category of loop spaces of open subsets in euclidean spaceNonlinear Analysis, 1991
- On p-convex sets and geodesicsJournal of Differential Equations, 1988
- Morse theory on Hilbert manifoldsTopology, 1963
- The Imbedding Problem for Riemannian ManifoldsAnnals of Mathematics, 1956