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.
Morbidelli, Modern Celestial Mechanics: Aspects of Solar System Dynamics (Taylor and Francis, 2002)
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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.