A Melnikov-Arnold integral procedure estimates sizes of secondary resonances of any order in the standard map up to the optimal normal form order without traditional normalization.
Fine structure of splitting of the separat rix of a nonlinear resonance,
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Melnikov-Arnold integrals and optimal normal forms
A Melnikov-Arnold integral procedure estimates sizes of secondary resonances of any order in the standard map up to the optimal normal form order without traditional normalization.