Dancer, E. Norman; Rybicki, Sławomir A note on periodic solutions of autonomous Hamiltonian systems emanating from degenerate stationary solutions. (English) Zbl 1015.34032 Differ. Integral Equ. 12, No. 2, 147-160 (1999). The authors give sufficient conditions for the existence of global bifurcations of nonstationary periodic solutions to Hamiltonian systems. These bifurcations are nontraditionally from degenerate critical points of Hamiltonians. The degree arguments for \(S^1\)-equivalent gradient maps are employed for this goal. Several illustrating examples are supplied. Reviewer: Jan Andres (Olomouc) Cited in 2 ReviewsCited in 11 Documents MSC: 34C25 Periodic solutions to ordinary differential equations 58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces 34C23 Bifurcation theory for ordinary differential equations 37G10 Bifurcations of singular points in dynamical systems Keywords:periodic solutions; global bifurcations; degenerate case; Hamiltonian systems; degree PDFBibTeX XMLCite \textit{E. N. Dancer} and \textit{S. Rybicki}, Differ. Integral Equ. 12, No. 2, 147--160 (1999; Zbl 1015.34032)