Degenerated singular cycles of inclination-flip type

Abstract In the present article we show that the elements of certain class of vector field cycles, called singular cycles, yield through two-parameter families a transition from simple to more complex systems. Our cycles here are more degenerate than the ones first described in [BLMP], due to a further nontransversal intersection between the invariant manifolds of the elements in the cycle. Bifurcation diagrams are provided, as well as hyperbolicity is proved to be prevalent for generic codimension-two perturbations of these degenerated cycles.