Abstract

We study bifurcations of invariant tori that are generated by the normal dynamics. The tori have to be quasi-periodic tori and we use Kolmogorov-Arnol’d-Moser (KAM) Theory, greatly inspired by Moser’s Modifying Term approach. The theory so becomes an interaction of Singularity Theory and KAM Theory, both extending and simplifying the quasi-periodic bifurcation theory as developed in the 1990's. We combine the conditions of KAM theory with the conditions of bifurcation theory into a quasi-periodic bifurcation theory where next to the most degenerate tori we simultaneously get all the branches of less degenerate tori of the same dimension.