We consider families of one and a half degrees of freedom Hamiltonians with high frequency periodic dependence on time, which are perturbations of an autonomous system.

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Baldomá et al. (Thu,) studied this question.

synapsesocial.com/papers/6a1bc9e0d54006be995efb57 https://doi.org/https://doi.org/10.1090/memo/0792

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1A Proof of the Exponentially Small Transversality of the Separatrices for the Standard Map1999 · 110 citations
2Exponentially Small Splitting of Separatrices Under Fast Quasiperiodic Forcing1997 · 79 citations
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5Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom1997 · 59 citations

Exponentially small splitting of invariant manifolds of parabolic points | Synapse

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1A Proof of the Exponentially Small Transversality of the Separatrices for the Standard Map1999 · 110 citations
2Exponentially Small Splitting of Separatrices Under Fast Quasiperiodic Forcing1997 · 79 citations
3An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum1992 · 108 citations
4Homoclinic orbits to parabolic points1997 · 12 citations
5Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom1997 · 59 citations