ANALYTICAL CONSTRUCTION OF HOMOCLINIC ORBITS OF TWO- AND THREE-DIMENSIONAL DYNAMICAL SYSTEMS

An approach for the construction of homoclinic orbits of non-linear dynamical systems with phase spaces of dimensions equal to two or three is proposed here. The non-linear Schrodinger equation and Lorenz system are considered. Quasi-Padeʹ approximants are used for this construction. Potentiality and convergence conditions used earlier in the theory of non-linear normal vibration modes make it possible to solve the boundary-value problems formulated for the orbits and to evaluate initial amplitude values.