Abstract
In this article, we review the construction of Hamiltonian perturbation theories with emphasis on Hori's theory and its extension to the case of dynamical systems with several degrees of freedom and one resonant critical angle. The essential modification is the comparison of the series terms according to the degree of homogeneity in both % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaacq% aH1oqzaSqabaaaaa!3699!\[\sqrt \varepsilon \]and a parameter which measures the distance from the exact resonance, instead of just % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaacq% aH1oqzaSqabaaaaa!3699!\[\sqrt \varepsilon \].
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Ferraz-Mello, S. On hamiltonian averaging theories and resonance. Celestial Mech Dyn Astr 66, 39–50 (1996). https://doi.org/10.1007/BF00048822
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DOI: https://doi.org/10.1007/BF00048822