97-250 C. Bonet, D. Sauzin, T.M. Seara, M. Valencia.

Adiabatic invariant of the Harmonic Oscillator, Complex Matching and Resurgence. (90K, LaTeX2e) Apr 30, 97

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Abstract. The linear oscillator equation with a frequency depending slowly on time is used to test a method to compute exponentially small quantities. This work present the matching method in the complex plane as a tool to obtain rigorously the asymptotic variation of the action of the associated hamiltonian {\sl beyond all orders}. The solution in the complex plane is aproximated by a series in which all terms present a singularity at the same point. Following matching techniques near this singularity one is led to an equation which does not depend on any parameter, the so-called inner equation, of a Riccati type. This equation is studied by resurgence methods.

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