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A note on periodic solutions of autonomous Hamiltonian systems emanating from degenerate stationary solutions. (English) Zbl 1015.34032

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.

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
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