Chaotic orbits by Melnikov's method: A survey of applications

Marsden, J. E.

In Proc. IEEE Conf. on Dec. and Control, 22, (1983), 356-359

Abstract:

In this lecture I will survey a number of recent applications of Melnikov's method to a variety of interesting physical situations.
There are many modifications of the basic technique possible depending on the dimension of the system, whether or not dissipation or forcing are included or whether or not the system is autonomous. However to get the basic idea, it is useful to begin with a conservative but externally forced one degree of freedom Hamiltonian system. After presenting the basic theorem for this case in §2, we shall discuss the generalization of the theory in §3 and the various applications in §4.