- 09-121 M. Guardia, C. Olive, T. Seara
- Exponentially small splitting for the pendulum: a classical problem revisited
Jul 25, 09
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Abstract. In this paper, we study the classical problem of the exponentially
small splitting of separatrices of the rapidly forced pendulum.
Firstly, we give an asymptotic formula for the distance between the
perturbed invariant manifolds in the so-called singular case and we
compare it with the prediction of Melnikov Theory. Secondly, we give
exponentially small upper bounds in some cases in which the
perturbation is bigger than in the singular case and we give some
heuristic ideas how to obtain an asymptotic formula for these cases.
Finally, we study how the splitting of separatrices behaves when the
parameters are close to a codimension-2 bifurcation point.