Abstract
The rapidly forced pendulum equation with forcing δ sin t/ε, where δ = δ0 εp, p = 5, for δ0, ε sufficiently small, is considered. We sketch our proof that stable and unstable manifolds split and that the splitting distance d(t0) in the ẋ-t plane satisfies
and the angle of transversal intersection, ψ, in the t = 0 section satisfies
.
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M. Kummer, J.A. Ellison and A.W. Saenz, to be submitted.
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© 1991 Plenum Press, New York
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Kummer, M., Ellison, J.A., Sáenz, A.W. (1991). Exponentially Small Phenomena in the Rapidly Forced Pendulum. In: Segur, H., Tanveer, S., Levine, H. (eds) Asymptotics beyond All Orders. NATO ASI Series, vol 284. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0435-8_14
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DOI: https://doi.org/10.1007/978-1-4757-0435-8_14
Publisher Name: Springer, Boston, MA
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