Geodesic
On the Analytic Solvability of the Problem of Distinguishing between Center and Focus
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear analytic differential equations, Tome 254 (2006), pp. 11-100

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The analytic solvability of the problem of distinguishing between a center and a focus is proved in each of semialgebraic subsets whose union is the entire set of monodromic germs. 
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     author = {N. B. Medvedeva},
     title = {On the {Analytic} {Solvability} of the {Problem} of {Distinguishing} between {Center} and {Focus}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {11--100},
     publisher = {mathdoc},
     volume = {254},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_254_a1/}
}
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N. B. Medvedeva. On the Analytic Solvability of the Problem of Distinguishing between Center and Focus. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear analytic differential equations, Tome 254 (2006), pp. 11-100. http://geodesic.mathdoc.fr/item/TM_2006_254_a1/