Detecting the limit cycles for a class of Hamiltonian systems under thirteen-order perturbed terms

Abstract

It this paper we study a class of perturbed Hamiltonian systems under perturbations of thirteen order in order to detect the number of limit cycles which bifurcate from some periodic orbits of the unperturbed Hamiltonian system. The system has been previously studied in \cite{tig2}, \cite{tig3}, \cite{tig4}. We observe in the present work that the system under perturbations of thirteen order can have more limit cycles than under perturbations of five \cite{tig3}, respectively nine \cite{tig4} order but we have not identified more limit cycles than under perturbations of seven \cite{tig2} order.