Homoclinic orbits for a class of first order nonperiodic Hamiltonian systems.

In this paper we study the existence of infinitely many homoclinic orbits for a class of first order Hamiltonian systems z ̇ = J H z ( t , z ) , where the Hamiltonian function H ( t , z ) is nonperiodic in t and only locally defined near the origin with respect to z . Under some mild conditions on H , we show that these Hamiltonian systems possess a sequence of homoclinic orbits near the origin. [ABSTRACT FROM AUTHOR]