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Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems. (English) Zbl 1192.34035
Among all quasi-homogeneous polynomial vector fields on the plane, the authors characterize which ones are monodromic (that is, admit a Poincaré first return map in a neighborhood of the origin). Among monodromic systems they give conditions that distinguish foci from centers. Finally, they characterize integrability of such systems.
##### MSC:
 34C05 Location of integral curves, singular points, limit cycles (ODE) 34C07 Theory of limit cycles of polynomial and analytic vector fields
##### Keywords:
quasi-homogeneous vector field; monodromy