An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, devising an expansion for the splitting matrix associated with a. homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing hyperbolicity by a shift-of-contour argument. An exponentially small upper bound on the splitting is implied. The focus of this paper is on the method. (C) 2010 American Institute of Physics. [doi:10.1063/1.3398483]