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. © 2010 American Mathematical Society.
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 1 Jan 2011|
- Abelian integral
- Chebyshev system
- Hamiltonian perturbation
- Limit cycle
- Planar vector field