Global phase portraits and bifurcation diagrams for reversible equivariant hamiltonian systems of linear plus quartic homogeneous polynomials

This paper is devoted to the complete classification of global phase portraits for reversible equivariant Hamiltonian systems of linear plus quartic homogeneous polynomials. Such system is affinely equivalent to one of five normal forms by an algebraic classification of its infinite singular points. Then, we classify the global phase portraits of these normal forms on the Poincare disc. There are exactly \begin{document}$ 13 $\end{document} different global topological structures on the Poincare disc. Finally we provide the bifurcation diagrams for the corresponding global phase portraits.