Abstract
In this paper we give a statistical description of the phase space of a Fermi–Pasta–Ulam chain using the Fast Lyapunov Indicator, looking for properties valid in the thermodynamic limit.
Similar content being viewed by others
References
Bambusi D. and Ponno A. (2006). On metastability in FPU. Commun. Math. Phys. 264(2): 539–561
Berchialla L., Galgani L. and Giorgilli A. (2004a). Localization of energy in FPU chains. Discrete Contin. Dyn. Syst. 11(4): 855–866
Berchialla L., Giorgilli A. and Paleari S. (2004b). Exponentially long times to equipartition in the thermodynamic limit. Phys. Lett. A 321(3–4): 167–172
Bocchieri P., Scotti A., Bearzi B. and Loinger A. (1970). Anharmonic chain with Lennard–Jones interaction. Phys. Rev. A 2: 2013–2019
Carati, A., Galgani, L., Giorgilli, A., Paleari, S.: Fermi–Pasta–Ulam phenomenon for generic initial data. Phys. Rev. E 76(2), 022104. doi:10.1103/PhysRevE.76.022104, http://link.aps.org/abstract/PRE/v76/e022104 (2007)
Cercignani C., Galgani L. and Scotti A. (1972). Zero-point energy in classical nonlinear mechanics. Phys. Lett. A 38: 403–404
Fermi, E., Pasta, J., Ulam, S.: Studies of nonlinear problems. Los Alamos document LA-1940 (1955) (repr. The Collected Papers of Enrico Fermi. Vol. II: U.S. 1939–1954, University of Chicago Press, 1965)
Froeschlé C., Gonczi R. and Lega E. (1997a). The Fast Lyapunov indicator: a simple tool to detect weak chaos. Application to the structure of the main asteroidal belt. Planet. Space Sci. 45(7): 881–886
Froeschlé C., Lega E. and Gonczi R. (1997b). Fast Lyapunov indicators. Application to asteroidal motion. Celest. Mech. Dyn. Astron. 67(1): 41–62
Froeschlé C., Guzzo M. and Lega E. (2000). Graphical evolution of the Arnold web: from order to chaos. Science 289: 2108–2110
Froeschlé C., Guzzo M. and Lega E. (2006). Analysis of the chaotic behaviour of orbits diffusing along the Arnold’s web. Celes. Mech. Dyn. Astron. 95: 141–153
Fucito F., Marchesoni F., Marinari E., Parisi G., Peliti L., Ruffo S. and Vulpiani A. (1982). Approach to equilibrium in a chain of nonlinear oscillators. J. Phys. 43(5): 707–713
Galgani L and Scotti A. (1972). Planck-like distributions in classical nonlinear mechanics. Phys. Rev. Lett. 28: 1173–1176
Giorgilli A., Paleari S. and Penati T. (2005). Local chaotic behaviour in the FPU system. Discrete Contin. Dyn. Syst. Ser. B 5(4): 991–1004
Guzzo M., Lega E. and Froeschlé C. (2002). On the numerical detection of the effective stability of chaotic motions in quasi-integrable systems. Phys. D 163(1–2): 1–25
Guzzo M., Lega E. and Froeschlé C. (2006). Diffusion and stability in perturbed non-convex integrable systems. Nonlinearity 19(5): 1049–1067
Henrici A., Kappeler T. (2008) Results on normal forms for FPU chains. Comm. Math. Phys. doi: 10.1007/s00220-007-0387-z (2008) (to appear)
Izrailev F.M. and Chirikov B.V. (1966). Stochasticity of the simplest dynamical model with divided phase space. Sov. Phys. Dokl. 11(1): 30
Lorenzoni P. and Paleari S. (2006). Metastability and dispersive shock waves in the Fermi–Pasta–Ulam system. Phys. D 221(2): 110–117
Paleari, S, Penati, T.: Equipartition times in a Fermi–Pasta–Ulam system. Discrete Contin. Dyn. Syst. Suppl. (Intl. Conf. Dynamical Systems and Differential Equations, Pomona, CA, 2004), 710–719 (2005)
Pettini M. and Landolfi M. (1990). Relaxation properties and ergodicity breaking in nonlinear Hamiltonian dynamics. Phys. Rev. A. 41(2): 768–783
Zabusky N.J. and Kruskal M.D. (1965). Interaction of “solitons” in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15(6): 240–243
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Paleari, S., Froeschlé, C. & Lega, E. Global dynamical properties of the Fermi–Pasta–Ulam system. Celest Mech Dyn Astr 102, 241–254 (2008). https://doi.org/10.1007/s10569-008-9138-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10569-008-9138-5