The construction of homo- and heteroclinic orbits in non-linear systems

Padé and quasi-Padé approximants are used to construct homo- and heteroclinic orbits of non-linear systems. By using the convergence condition for Padé approximants and the conditions at infinity the problem can be solved with sufficiently high accuracy. Actual computations are carried out for the non-autonomous Duffing equation, the equations of vibrations of a parametrically driven mathematical pendulum, and the van der Pol-Duffing equation with non-linear elastic characteristic.