NUMERICAL CONTINUATION OF CONNECTING ORBITS AND THEIR TANGENCIES

We present new or improved methods to continue heteroclinic and homoclinic orbits to fixed points in iterated maps and to compute their fold bifurcation curves, corresponding to the tangency of the invariant manifolds. To compute these orbits, first we need to compute transversal intersection of two invariant stable and unstable manifolds. The proposed methods are applicable to general n-dimensional maps and are implemented in MATLAB. They are based on the continuation of invariant subspaces (CIS) algorithm, which is presented in a novel way.