An indicator of chaos based on the equal-potential curves in 2D Hamiltonian flows

Abstract

We prove that the 2D Hamiltonian system is unstable if its potential satisfies ∂2V∂r2>0 and some segments of equal-potential curves concave toward the origin in the physically accessible region for a given E. And we present a new indicator of chaos based on the equal-potential curves. We show that our criterion gives the results in good agreement with that of the technique of surface of section. It provides a new insight into the relationship between the geometrical picture and the instability for the 2D Hamiltonian dynamical systems. Finally we detect the chaotic behavior for some important potentials, and show our results in good agreement with the Poincaré plots and the new geometric criterion of HBLSL.