We present a criterion that provides an easy sufficient condition in order for a collection of Abelian integrals to have the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be checked, in many cases, in a purely algebraic way. By using this criterion, several known results are obtained in a shorter way and some new results, which could not be tackled by the known standard methods, can also be deduced.

Unfolding of a quadratic integrable system with a homoclinic loop

Lin Ping Peng

Acta Mathematica Sinica • 2002

Weigu Li

A. Gasull

J. Llibre and Zhifen Zhang, Chebyshev property of complete elliptic integrals and its application to Abelian integrals, Pacific J. Math. 202 (2002) 341–361. MR1887769 • 2002

Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles