Hamiltonian chaos and differential geometry of configuration space–time

This paper tackles Hamiltonian chaos by means of elementary tools Riemannian geometry. More precisely, a flow is identified with geodesic on configuration space-time endowed suitable metric due to Eisenhart. Until now, this framework has never been given attention describe chaotic dynamics. A gap that filled in the present work. In Riemannian-geometric context, stability/instability dynamics depends curvature properties ambient manifold and investigated Jacobi--Levi-Civita (JLC) equation for spread. It confirmed dominant mechanism at ground parametric instability variations along geodesics. comparison reported outcomes JLC written also Jacobi space another Eisenhart an extended space-time. applied H\'enon-Heiles model, two-degrees freedom system. Then study 1D classical Heisenberg XY model large number degrees freedom. Both advantages drawbacks geometrization are discussed. Finally, quick hint put forward concerning possible extension differential-geometric investigation generic dynamical systems, including dissipative ones, resorting Finsler manifolds.