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An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum. (English) Zbl 1311.70024

Summary: 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.{
©2010 American Institute of Physics}

MSC:

70F20 Holonomic systems related to the dynamics of a system of particles
70H05 Hamilton’s equations
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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