Bifurcation of invariant tori from a periodic motion under singular perturbations

Abstract

We study singular periodic perturbations of a differential-algebraic system that admits a periodic solution. We consider the problem on the bifurcation of an invariant torus from the periodic solution as the small parameter ɛ multiplying the derivative passes through zero. We construct a bifurcation equation, whose positive root corresponds to an invariant torus with amplitude of the order of $\sqrt \varepsilon $ .