Limit Cycles Of Some Z₃-Equivariant Near-Hamiltonian Polynomial Systems

As an introduction, in the first chapter we introduce the background of our research and main topics that we will study in the following chapters. We also give a description of our methods and results obtained in this thesis in the first chapter.In the second chapter. we give some basic definitions and also introduce some known results as lemmas. We give several expansions of Melnikov functions which play an important role in our study.In the third chapter, our main purpose is to study the number of limit cycles and their distribution of some near-Hamiltonian polynomial systems. We discuss the number of limit cycles for Z₃—equivariant polynomial systems with degree 3, 4 and degree 5 by perturbing a cubic system, obtaining 4, 10 and 15 limit cycles respectively.In the forth chapter, we study the number of another kind of Z₃—equivariant system. We prove that 5 and 6 limit cycles can exist under perturbation of degree 3 and 4 respectively. For the cubic case we obtain one more limit cycle than [9] for the same kind of systems.