LYAPUNOV EXPONENTS FROM GEODESIC SPREAD IN CONFIGURATION-SPACE

The exact form of the Jacobi-Levi-Civita (JLC) equation for geodesic s pread is here explicitly worked out at arbitrary dimension for the con figuration space manifold M-E={q is an element of R-N\V(q)<E} of a sta ndard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric g(J). As the Hamiltonian flow corresponds to a geodesic flow o n (M-E, g(J)), the JLC equation can be used to study the degree of ins tability of the Hamiltonian flow. It is found that the solutions of th e JLC equation are closely resembling the solutions of the standard ta ngent dynamics equation which is used to compute Lyapunov exponents. T herefore the instability exponents obtained through the JLC equation a re in perfect quantitative agreement with usual Lyapunov exponents. Th is work completes a previous investigation that was limited only to tw o degrees of freedom systems.