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Bifurcation of critical periods for plane vector fields. (English) Zbl 0678.58027
A bifurcation problem in families of plane vector fields which have a nondegenerate center at the origin for all values of a parameter $$\lambda \in {\mathbb{R}}^ N$$ is studied. In particular, for such a family, the period function $$(\xi,\lambda)\to P(\xi,\lambda)$$ is defined; it assigns the minimum period to each member of the continuous band of periodic orbits surrounding the origin. The bifurcation problem is to determine the critical points of this function near the center with $$\lambda$$ as bifurcation parameter. The obtained results are applied to the quadratic systems with Bautin centers and to one degree of freedom $$kinetic+potential''$$ Hamiltonian systems with polynomial potentials.
Reviewer: J.Šiška

##### MSC:
 37G99 Local and nonlocal bifurcation theory for dynamical systems 37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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