On the number of zeros of Abelian integrals for discontinuous quadratic differential systems

arXiv1705.05057MaRDI QIDQ6286664

Shiyou Sui, Jihua Yang, Liqin Zhao

Publication date: 14 May 2017

Abstract: Applying the Picard-Fuchs equation to the discontinuous differential system, we obtain the upper bounds of the number of zeros for Abelian integrals of four kinds of quadratic differential systems when it is perturbed inside all discontinuous polynomials with degree $n$. Furthermore, by using the {it Chebyshev criterion}, we obtain the sharp upper bounds on each period annulus for $n=2$.

Mathematics Subject Classification ID

Qualitative theory for ordinary differential equations (34Cxx)

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