Homoclinic orbits of invertible maps

In this paper, we present a systematic method for finding all homoclinic orbits of invertible maps in any finite dimension. One advantage of this method is that it can also be used to order and classify all the homoclinic orbits, using symbolic dynamics, if a certain criterion is satisfied. We also present a more direct scheme, which quickly locates homoclinic orbits without, however, being able to order and classify them. Our work represents an extension of a method introduced in an earlier paper, with which one could only find homoclinic orbits possessing a certain symmetry. Thus, asymmetric homoclinic orbits can now be as easily computed. One application of our results is the explicit construction of breather (and multibreather) solutions of,a class of one-dimensional nonlinear lattices.