山中 祥五 氏
We consider a class of two-degree-of-freedom Hamiltonian systems with saddle-centers connected by heteroclinic orbits. We show that if the sufficient conditions for real-meromorphic nonintegrability hold, then the stable and unstable manifolds of the periodic orbits intersect transversely, are quadratically tangent or do not intersect in general, and they do not intersect when the Hessian matrix of the Hamiltonian has a different number of positive eigenvalues at the associated saddle-centers. Our theory is illustrated for a system with quartic single-well potential. This is a joint work with Prof. Kazuyuki Yagasaki.