Indicator of chaos based on the Riemannian geometric approach.

Using the Riemannian geometric approach to Hamiltonian systems, we show that the empirical indicator of chaos proposed by Kosloff and Rice [J. Chem. Phys. 74, 1947 (1981)], an improved version of the well-known Toda-Brumer criterion, is equivalent to sectional curvature of the Jacobi equation when the Eisenhart metric is chosen for the Riemannian manifold. Further, we present a relation among the sectional curvature, the Lyapunov exponents, and the Kolmogorov-Sinai entropy. By using this relation, the empirical indicator by Kosloff and Rice, which is local, can be used as a global indicator of chaos.