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Symmetric centers on planar cubic differential systems. (English) Zbl 1472.34059

The authors of this paper investigate the simultaneous existence of centers in symmetric planar polynomial differential systems. In particular, they present necessary and sufficient conditions for the existence of a bi-center of four families for real cubic symmetric systems and obtain the conditions for the isochronicity of such bi-centers.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34C14 Symmetries, invariants of ordinary differential equations

Software:

SINGULAR; primdec
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