Perpustakaan Digital ITB

Transversal intersections between stable and unstable manifolds of an equilibrium (or a fixed point) of a dynamical system might induce chaotic dynamics. The Melnikov's Method is developed to prove the existence of transversal intersection between those manifolds in a perturbation of planar Hamiltonian systems. We generalize this method for dealing with perturbations of n-degree of freedom Hamiltonian systems. The construction involves several classical results, such as the Smale Horseshoe, the Conley-Moser condition, and the Smale-Birkhoff Homoclinic theorem. We present two examples where one of them provides positive result and the other one provides negative result.