In dynamics problem on 3 dimensional manifold, a global surface of section is useful tool for study periodic orbits provided it exists. In general, it is hard to find and moreover it is hard to know whether it exists. In Hamiltonian dynamics on R^4, there is a useful criterion for the existence of a disk-like global surface of section for the Hamiltonian vector field that is dynamically convexity. In this talk, we will study about the dynamically convex and the relationship with the strictly convexity.