Authors:
Ronald Adams and J.D. Mireles James

Abstract: Validated numerical computations are used to study one parameter branches of connecting orbits and their bifurcations. The idea is to formulate the connecting orbit as a zero of a certian finite dimensional map. Computer assisted methods of proof for continuation and bifurcation of zeros are applied to the map, providing global results for the underlying dynamical system. We use the parameterization method to represent the local stable/unstable manifolds of the fixed point, and focus on the example of the Henon map.