Nonconnected heterodimensional cycles: bifurcation and stability

Abstract

The authors study arcs of diffeomorphisms that bifurcate through the creation of a nonconnected heterodimensional cycle. They exhibit two open sets of such arcs; in the first one, after the bifurcation, the set of parameter values for which the corresponding diffeomorphism is stable (stable set) is empty, in the second one Omega -stability has some degree of prevalence, i.e. the relative measure of the Omega -stable set is bounded away from zero.