A method for locating symmetric homoclinic orbits using symbolic dynamics

In this paper we present a method which can identify and locate symmetric h omoclinic orbits in a homoclinic tangle formed by the intersecting stable a nd unstable manifolds of a symmetric 2D map. The method consists of a syste matic search in parameter space and determination of the order in which the se orbits arise using symbolic dynamics. Each orbit corresponds to a unique sequence and it is computed by iterating the map along the unstable manifo ld to match a specific symmetry at the middle of the orbit. An application of the method to the determination of multibreather solutions of 1D lattice s is discussed.