On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systems
The authors consider second order Hamiltonian systems on complete Riemannian manifolds of the form \(D_ t \dot x(t) + \text{grad}_ x V(t,x(t)) = 0\), where the potential \(V\) is \(T\)-periodic in \(t\). They prove the existence of infinitely many homoclinic orbits.
second order Hamiltonian systems on complete Riemannian manifolds
scientific article; zbMATH DE number 736828