We present a numerical method for finding all homoclinic orbits of an invertible map in any dimension. The method has completely controllable accuracy and is capable of uniquely identifying and naming each homoclinic orbit.
Homoclinic orbits are presented as a useful tool for obtaining breather solutions (time periodic, spatially localized) of one dimensional nonlinear lattices (Klein Gordon, FPU and mixed). We present how the relationship between homoclinic orbits and breathers is formed, and advantages of using this method for obtaining breathers over the traditional method of continuation.