Computing center conditions for vector fields with constant angular speed

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摘要

We investigate the planar analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The conditions for the origin to be a center (in fact, an isochronous center) are obtained. Concretely, we find conditions for the existence of a Cw-commutator of the field. We cite several subfamilies of centers and obtain the centers of the cuartic polynomial systems and of the families (−y+x(H1+Hm),x+y(H1+Hm))t and (−y+x(H2+H2n),x+y(H2+H2n))t, with Hi homogeneous polynomial in x,y of degree i. In these cases, the maximum number of limit cycles which can bifurcate from a fine focus is determined.

论文关键词:34C05,34C25,Limit cycles,Periodic solutions

论文评审过程:Received 1 December 2001, Revised 12 July 2002, Available online 31 December 2002.

论文官网地址:https://doi.org/10.1016/S0377-0427(02)00818-X