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 $H:\mathbb R^4 \to \mathbb R$ 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 $H^{-1}(0)$.