Lyapunov exponents from geodesic spread in configuration space
Monica Cerruti-Sola, Roberto Franzosi, Marco Pettini
Abstract
The exact form of the Jacobi -- Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold ME = q in RN | V(q) < E of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric gJ. As the Hamiltonian flow corresponds to a geodesic flow on (ME,gJ), the JLC equation can be used to study the degree of instability of the Hamiltonian flow. It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. This work completes a previous investigation that was limited only to two-degrees of freedom systems.
Create a lesson
Related papers
Chaotic eigenfunctions in phase space
S. Nonnenmacher, A. Voros
Improved control of delayed measured systems
Jens Christian Claussen, Heinz Georg Schuster
The accurate and comprehensive model of thin fluid flows with inertia on curved substrates
A. J. Roberts, Zhenquan Li
On periodic solutions of a Hamilton-Jacobi equation with periodic forcing
Andrei Sobolevskii
Drifters dispersion in the Adriatic Sea: Lagrangian data and chaotic model
Guglielmo Lacorata, Erik Aurell, Angelo Vulpiani
Generalized multibaker maps for open dissipative systems
Z. Kaufmann, P. Szépfalusy