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Bifurcation of critical periods for planar Hamiltonian systems of degree $$2n-1$$. (English) Zbl 1212.37077
Summary: The orders of weak centers are determined for a family of planar Hamiltonian systems of degree $$2n-1$$ where only odd degree nonlinearities are included and the lowest degree is $$2m-1$$. Moreover, local bifurcation of critical periods is studied and it is proved that at most $$m-1$$ local critical periods can be produced and the maximum number is achievable.
MSC:
 37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 34C23 Bifurcation theory for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations