A CHEBYSHEV CRITERION FOR ABELIAN INTEGRALS

作者：Grau M^*; Manosas F; Villadelprat J

来源：Transactions of the American Mathematical Society, 2011, 363(1): 109-129.

DOI：10.1090/S0002-9947-2010-05007-X

• Planar vector field
• Hamiltonian perturbation
• limit cycle
• Chebyshev system
• Abelian integral

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.

• 出版日期2011-1