ON THE NUMBER OF ZEROS OF ABELIAN INTEGRAL FOR A CUBIC ISOCHRONOUS CENTER.

In this paper, we study the number of limit cycles that bifurcate from the periodic orbits of a cubic reversible isochronous center under cubic perturbations. It is proved that in this situation the least upper bound for the number of zeros (taking into account the multiplicity) of the Abelian integral associated with the system is equal to four. Moreover, for each k = 0, 1, ..., 4, there are perturbations that give rise to exactly k limit cycles bifurcating from the period annulus. [ABSTRACT FROM AUTHOR]