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The center-focus problem for a system with homogeneous nonlinearities in the case of zero eigenvalues of the linear part. (English. Russian original) Zbl 1067.34030

Differ. Equ. 39, No. 2, 155-164 (2003); translation from Differ. Uravn. 39, No. 2, 147-158 (2003).
The authors consider the center-focus problem for system \[ \dot x=y+X_{2n+1}(x,y),\quad \dot y=Y_{2n+1}(x,y).\tag{1} \] They solve the center-focus problem for system (1) for \(n=3\) using the formal series method and prove the existence of systems (1) for \(n=1,2,3\) with 2, 5 and 9 limit cycles, respectively, in a neighborhood of the origin.
Reviewer: Jihong Dou (Xian)

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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