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arXiv · 1110.1698

Limit cycles for planar semi-quasi-homogeneous polynomial vector fields

Yulin Zhao
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Abstract

This paper is concerned with the limit cycles for planar semi-quasi-homogeneous polynomial systems. We give some explicit criteria for the nonexistence and existence of periodic orbits. Let $N=N(p,q,m,n)$ be the maximum number of limit cycles of such system. A lower bound is given for $N=N(p,q,m,n)$. The cyclicity and center problem are studied for some subfamilies of semi-quasi-homogeneous polynomial systems. Our results generalize those obtained for polynomial semi-homogeneous systems.

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Yulin Zhao. 2011-10-08. Limit cycles for planar semi-quasi-homogeneous polynomial vector fields. https://arxiv.org/abs/1110.1698

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