Geodesic
Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries
Electronic Journal of Differential Equations, Tome 1999 (1999).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper deals via variational methods with the existence of infinitely many homoclinic orbits for a class of the first-order time-dependent Hamiltonian systems $$ \dot{z}=JH_z(t,z) $$ without any periodicity assumption on $H$, providing that $H(t,z)$ is G-symmetric with respect to $z\in {\Bbb R}^{2N}$, is superquadratic as $|z|\to\infty$, and satisfies some additional assumptions.
Classification : 34B30, 34C37
Keywords: Hamiltonian system, homoclinic orbits 
@article{EJDE_1999__1999__a15,
     author = {Lee, Cheng},
     title = {Infinitely many homoclinic orbits for {Hamiltonian} systems with group symmetries},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1999},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a15/}
}
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Lee, Cheng. Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries. Electronic Journal of Differential Equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a15/