In this paper we present a method which can identify and locate symmetric homoclinic orbits in a homoclinic tangle formed by the intersecting stable and unstable manifolds of a symmetric 2D map. The method consists of a systematic search in parameter space and determination of the order in which these orbits arise using symbolic dynamics. Each orbit corresponds to a unique sequence and it is computed by iterating the map along the unstable manifold to match a specific symmetry at the middle of the orbit. An application of the method to the determination of multibreather solutions of 1D lattices is discussed.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)