Lyapunov exponents from geodesic spread in configuration space
Anno: 1997
Autori: Cerruti-Sola M., Franzosi R., Pettini M.
Affiliazione autori: Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, Firenze, 50125, Italy; Dipartimento di Fisica, Università di Firenze, Largo E. Fermi 5, Firenze, 50125, Italy; Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, Firenze, 50125, Italy
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 [Formula Presented] of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric [Formula Presented] As the Hamiltonian flow corresponds to a geodesic flow on [Formula Presented] 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.
Giornale/Rivista: PHYSICAL REVIEW E
Volume: 56 (4) Da Pagina: 4872 A: 4875
Parole chiavi: Choas; Differential Geometry; Dynamical SystemsDOI: 10.1103/PhysRevE.56.4872Citazioni: 15dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2024-05-05Riferimenti tratti da Isi Web of Knowledge: (solo abbonati) Link per visualizzare la scheda su IsiWeb: Clicca quiLink per visualizzare la citazioni su IsiWeb: Clicca qui