Abstract
This paper deals with the bifurcation of critical periods from a rigidly quartic isochronous center. It shows that under any small homogeneous perturbation of degree four, up to any order in [Formula: see text], there are at most two critical periods bifurcating from the periodic orbits of the unperturbed system, and the upper bound is sharp. In addition, we further prove that under any small polynomial perturbation of degree [Formula: see text], up to the first order in [Formula: see text], there are at most [Formula: see text] critical periods bifurcating from the periodic orbits of the unperturbed quartic system.
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