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Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial. (English) Zbl 0921.34032

The authors study the isochronous centers of two-dimensional autonomous systems in the plane

x ˙=-y+X s (x,y),y ˙=x+Y s (x,y),

where X s (x,y) and Y s (x,y) are homogeneous polynomials of degree s=4· A center is isochronous if the period of all integral curves in a neighborhood of the origin is constant. Necessary conditions for such isochronous center are obtained. Reversible systems that have an isochronous center at the origin are studied.

MSC:
34C05Location of integral curves, singular points, limit cycles (ODE)
34A05Methods of solution of ODE