Abstract
Transformation properties of perturbation expansions of vibrational quasi-periodic orbits upon the modular transformations of frequencies are studied, using simple but nontrivial examples: the Siegel complex quadratic map and special solutions of the real area-preserving quadratic map. It is shown that the transformation properties are similar to those in the previously studied case of the rotational invariant tori, except for some special features of the real map, related to the atypical nature of 1/3 resonance in this case.
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