For small-energy Hénon-Heiles orbits, the slow variables u and w rotate with explicit formulas (17) and (58) that stay accurate for n ε^(5/2) << 1, far beyond the ε^(-2) validity of naive perturbation series.
and Weiss, J., 1982
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Long time evolution of the H\'enon-Heiles system for small energy
For small-energy Hénon-Heiles orbits, the slow variables u and w rotate with explicit formulas (17) and (58) that stay accurate for n ε^(5/2) << 1, far beyond the ε^(-2) validity of naive perturbation series.