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A parametrised version of Moser’s modifying terms theorem. (English) Zbl 1214.37023

One score of the paper is to derive a modifying terms theorem for parametrized families of vector fields, incorporating results on smoothness and Gevrey-regularity. A second motivation is to make the result a convenient tool for quasi-periodic bifurcation theory. As an application, it is given the analysis of the persistence of tori in the quasi-periodic Bogdanov-Takens bifurcation.

MSC:

37C55 Periodic and quasi-periodic flows and diffeomorphisms
37G99 Local and nonlocal bifurcation theory for dynamical systems
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