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 Volume 9, Number 3, 2019, Pages 943-961 Limit cycles for two classes of planar polynomial differential systems with uniform isochronous centers Bo Huang,Wei Niu Keywords:Averaging method, homogeneous polynomial, limit cycle, period solutions, uniform isochronous center. Abstract: In this article, we study the maximum number of limit cycles for two classes of planar polynomial differential systems with uniform isochronous centers. Using the first-order averaging method, we analyze how many limit cycles can bifurcate from the period solutions surrounding the centers of the considered systems when they are perturbed inside the class of homogeneous polynomial differential systems of the same degree. We show that the maximum number of limit cycles, $m$ and $m+1$, that can bifurcate from the period solutions surrounding the centers for the two classes of differential systems of degree $2m$ and degree $2m+1$, respectively. Both of the bounds can be reached for all $m$. PDF      Download reader