title: On the geometric formulation of Hamiltonian dynamics.
abstract: Under a proper assignment of a metric and a connection, the (classical) dynamical trajectories can be identified as geodesics of the underlying manifold. We show how these geometric structures can be derived; specifically, we construct them explicitly for configuration and phase spaces of Hamiltonian systems. We demonstrate how the correspondence between geometry and dynamics can be applied to study the conserved quantities of a dynamical system. Lastly, we demonstrate how the mean-curvature of the energy level-sets in phase-space might be correlated with strongly chaotic behavior.
authors.affiliation: Department of Mathematics, the Technion, Haifa 32000, Israel. calderon@tx.technion.ac.il
authors.forename: Eran
authors.initials: E
authors.lastname: Calderon
authors.forename: Lawrence
authors.initials: L
authors.lastname: Horwitz
authors.forename: Raz
authors.initials: R
authors.lastname: Kupferman
authors.forename: Steven
authors.initials: S
authors.lastname: Shnider
mesh_terms: D003198:Computer Simulation; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D013997:Time Factors