Centers with degenerate infinity and their commutators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:278

Article

Algaba, A ; Reyes, M

关键词: centers;    isochronous centers;    commutators;   

DOI  :  10.1016/S0022-247X(02)00625-X

来源: Elsevier

【 摘 要 】

We study polynomial systems with degeneracy at infinity and a center-focus equilibrium at the origin. We give some general properties related to the existence of polynomial commutators and use these properties in order to characterize uniformly isochronous polynomial centers with polynomial commutator and, also, we show that the commutator of the centers of the analytic systems whose angular speed is constant can be chosen of radial form. Finally, we characterize the systems (-y + P-s + Sigma(j=k)(n-1) x H-j, x + Q(s) +Sigma(j=k)(n-1) yH(j))(t) with polynomial commutator, with P-j, Q(j), H-j and K-j homogeneous polynomials. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free