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The period function for Hamiltonian systems with homogeneous nonlinearities. (English) Zbl 0891.34033

Authors’ abstract: The paper deals with Hamiltonian systems with homogeneous nonlinearities. We prove that such systems have no isochronous centers, that the period annulus of any of its centres is either bounded or the whole plane and that the period function associated to the origin has at most one critical point.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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