Vanderbauwhede, A. Bifurcation of subharmonic solutions. A generic approach. (English) Zbl 0557.34040 Differential equations, Proc. Conf., Birmingham/Ala. 1983, North-Holland Math. Stud. 92, 545-552 (1984). Summary: [For the entire collection see Zbl 0539.00010.] 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 [V. I. Arnol’d, Chapitres supplémentaires de la théorie des équations différentielles ordinaires (1980; Zbl 0455.34001)]; when restricting to one-parameter problems one obtains results similar to those of G. Iooss and D. Joseph [Elementary stability and bifurcation theory (1980; Zbl 0443.34001)]. Cited in 2 Documents MSC: 34C25 Periodic solutions to ordinary differential equations Keywords:abstract bifurcation; example; bifurcation of subharmonic solutions; Arnol’d tongues Citations:Zbl 0539.00010; Zbl 0455.34001; Zbl 0443.34001 PDFBibTeX XML