In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n+k-1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way. © 2011 Elsevier Inc.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Sep 2011|
- Abelian integral
- Chebyshev system
- Hamiltonian perturbation
- Limit cycle