Quasi-periodic saddle-node bifurcations near a differentiable singularity for forced oscillations (Q1329273)

From author's summary: ``In the Bogdanov-Takens singularity with reflection symmetry there is a curve \(\Gamma\) in parameter space such that all one-parameter paths that cross \(\Gamma\) transversally give saddle-node bifurcations of periodic orbits. In the analogous situation for periodically forced systems, the curve \(\Gamma\) is replaced by a Cantor set \(\widetilde\Gamma\) of parameter values that corresponds to nonhyperbolic quasi-periodic tori, and there is a restricted set of one- parameter paths that give quasi-periodic saddle-node bifurcations of tori. The proof requires finite differentiability of the system and uses a version of the Nash-Moser implicit function theorem''.