Study of a curvature-based criterion for chaos in Hamiltonian systems with two degrees of freedom

A non-Euclidean geometric criterion for chaos (Horwitz et al 2007 Phys. Rev. Lett. 98 234301) is investigated in bound systems with two degrees of freedom. It is shown that the criterion is partly equivalent to a simpler indicator of chaos based on the shape of equipotential curves. The method is numerically tested in a restricted Bohr model and in an extended Creagh–Whelan model. Although in some cases the geometric criterion approximately predicts the onset of chaos at low energies, manifest counterexamples disproving its general applicability are demonstrated. (paper)