Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point

It is known that branches of homoclinic orbits emanate froma singular point of a dynamical system with a double zero eigenvalue(Takens-Bogdanov point). We develop a robust numerical methodfor starting the computation of homoclinic branches near sucha point. It is shown that this starting procedure relates tobranch switching. In particular, for a certain transformed problemthe homoclinic predictor is guaranteed to converge to the trueorbit under a Newton iteration.