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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
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