TRANSVERSAL HETEROCLINIC CYCLE AND ITS APPLICATION TO HENON MAPPING

Let M be a smooth differentiable manifold, and f a C’diffeomorphism. Suppose that p∈M is a hyperbolic fixed point of f. According to the well-known stable manifold theorem, W~u(p) and W~s(p) are C~r submanifolds of M. The λ-lemma stated below gives a property of W~u(p) and W~s(p), which characterizes W~u(p) and W~s(p) powerfully in many cases when transversality appears.