Ronghua Cheng

NEW UPPER BOUNDS ON THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR THREE PERTURBED QUADRATIC REVERSIBLE SYSTEMS

For the quadratic reversible systems $r12$, $r16$ and $r18$, when they are perturbed by arbitrary polynomial of degree $n$, we explore the new upper bounds on the number of zeros for their Abelian integrals using the methods of Riccati equation and Picard-Fuchs equation. We consi...