Abstract
This paper is devoted to the cyclicity of a class of quadratic reversible systems with hyperelliptic level curves and two period annuli. By a new Chebyshev criterion which is an extension of the method proposed by Liu and Xiao (2020) [20], we prove that the cyclicity of every period annulus is two and show at the same time the configuration of the limit cycles. This paper is, to the best of our knowledge, the first work on the cyclicity of quadratic reversible systems for the hyperelliptic case.
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