Resumen de The Exact Number of Limit Cycles in a Class of Cubic Isochronous Hamiltonian Systems

Jihua Yang, Qipeng Zhang

• This paper investigates the limit cycle problem for a class of cubic isochronous Hamiltonian systems, when they are perturbed inside of polynomials of degree n. A upper bound of the number of limit cycles is obtained using the Abelian integral. Moreover, this bound is sharp. The method for obtaining the algebraic structure of the Abelian integral differs from those in other literature.