Finsler geometric local indicator of chaos for single orbits in the Henon-Heiles Hamiltonian

Translating the dynamics of the Henon-Heiles Hamiltonian as a geodesic flow on a Finsler manifold, we obtain a local and synthetic geometric indicator of chaos (GIC), which represents a link between local quantities and asymp totic behavior of orbits and gives a strikingly evident, one-to-one, corres pondence between geometry and instability. Going beyond the results attaine d using the customary dynamical approach and improving also on the global c riteria established within the Riemannian framework, the GIC is able to dis criminate between regular and stochastic orbits on a given energy surface, simply on the basis of the value it assumes along a relatively small piece of the trajectory, without long integrations of the dynamics and without an y reference to a perturbation.