a Divison of Applied Mathematics, Box F, Brown University, Providence, RI 02912, USA
b Department of Applied Mechanics and Control and Dynamical Systems 104-44, Caltech, Pasadena, CA 91125, USA
Abstract:
In this paper we study the dynamics near resonant elliptic equilibria in three-degree-of-freedom Hamiltonian systems. The resonances we consider have multiplicity two, and the corresponding local normal form for the equilibrium is integrable at cubic order. We prove the existence of families of 3-tori and whiskered 2-tori with nearby chaotic dynamics in the quartic normal form. The whiskers of the 2-tori intersect in a non-trivial way giving rise to multi-pulse homoclinic and heteroclinic connections. These connections survive in the full system as orbits homoclinic to invariant 3-spheres.