Hopf bifurcation from infinity
A sufficient condition for a polynomial centre to be global
A sufficient condition is given in order that a centre of a polynomial planar autonomous system be a global centre.
Commutators and linearizations of isochronous centers
We study isochronous centers of some classes of plane differential systems. We consider systems with constant angular speed, both with homogeneous and nonhomogenous nonlinearities. We show how to construct linearizations and first integrals of such systems, if a commutator is known. Commutators are found for some classes of systems. The results obtained are used to prove the isochronicity of some classes of centers, and to find first integrals for a class of Liénard equations with isochronous centers....
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