Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $mathbb {R}^4$

In this article the authors study Hamiltonian flows associated to smooth functions $H:mathbb R^4 o mathbb R$ restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point $p_c$ in the zero energy level $H^{-1}(0)$.