Bifurcation of Subharndnic Solutions. A Generic Approach

In this contribution we consider abstract bifurcation problems having a trivial branch of solutions, and equivariant under a finite cyclic group action. An example is the bifurcation of subharmonic solutions. We obtain, under a generically satisfied transversality condition, an abstract version of the Arnol'd tongues [2]; when restricting to one-parameter problems one obtains results similar to those of Iooss and Joseph [5].