Localization of energy in FPU chains

Discrete and Continuous Dynamical Systems

Volumn 11, Issue 4, 2004, Pages 855-856

  Berchialla, Luisa ^a   Galgani, Luigi ^b   Giorgilli, Antonio ^a  

^a UNIVERSITY OF MILANO BICOCCA   (Italy)

^b Dipartimento di Matematica   (Italy)

Author keywords

FPU model; Nonlinear systems

Indexed keywords

EID: 13244295528     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2004.11.855     Document Type: Article

References (20)

1. E. Fermi, J. Pasta, J. and S. Ulam, Studies of nonlinear problems Los Alamos document LA-1940 (1955).
2. P.M. Izrailev and B.V. Chirikov, Stochasticity of the simplest dynamical model with divided phase space Dokl. Akad. Nauk. SSSR 166 (1966), 57; Sov. Phys. Dokl. 11 (1966), 30.
3. P.M. Izrailev and B.V. Chirikov, Stochasticity of the simplest dynamical model with divided phase space Dokl. Akad. Nauk. SSSR 166 (1966), 57; Sov. Phys. Dokl. 11 (1966), 30.
4. P. Bocchieri, A. Scotti, B. Bearzi and A. Loinger, Anharmonic chain with Lennard-Jones interaction Phys. Rev. A 2 (1970), 2013-2019.
5. L. Casetti, M. Cerruti-Sola, M. Pettini and E.G.D.Cohen, The Fermi-Pasta-Ulam problem revisited: Stochasticity thresholds in nonlinear Hamiltonian systems Phys. Rev. E 55 (1997), 6566-6574.
6. J. De Luca, A.J. Lichtenberg, and S. Ruffo, Energy transition and time scale to equipartition in the Fermi-Pasta-Ulam oscillator chain, Phys. Rev. E 51 (1995), 2877-2884.
7. J. De Luca, A.J. Lichtenberg and S. Ruffo, S.: Universal evolution to equipartition in oscillator chains, Phys. Rev E 54 (1996), 2329-2333 (1996).
8. J. De Luca, A.J. Lichtenberg, and S. Ruffo, Finite time to equipartition in the thermodynamic limit, Phys. Rev E 60 (1999), 3781-3786.
9. M.C. Carotta, C. Ferrario, G. Lo Vecchio, B. Carazza and L. Galgani, New phenomenon in the stochastic transition of coupled oscillators, Phys. Rev A 17 (1978), 786.
10. A. Giorgilli, Rigorous results on the power expansions for the integrals of a Hamiltonian system near an elliptic equilibrium point, Ann. Ist. H. Poincaré, 48 (1988), 423-439.
11. L. Galgani, A. Giorgilli, A. Martinoli and S. Vanzini, On the problem of energy equipartition for large systems of the Fermi-Pasta-Ulam type; analytical and numerical estimates, Physica D 59 (1992), 334-348.
12. H. Kantz, Vanishing stability thresholds in the thermodynamic limit of nonintegrable conservative systems, Physica D 39 (1989), 322-335.
13. H. Kantz, R. Livi and S. Ruffo: Equipartition thresholds in chains of anharmonic oscillators, J. Stat. Phys. 76 (1994), 627-643.
14. R. Livi, M. Pettini, S. Ruffo, M. Sparpaglione and A. Vulpiani, Relaxation to different stationary states in the Fermi-Pasta-Ulam model, Phys. Rev A 28 (1983), 3544-3552.
15. R. Livi, M. Pettini, S. Ruffo, M. Sparpaglione, and A. Vulpiani, Equipartition threshold in nonlinear large Hamiltonian systems: the Fermi-Pasta-Ulam model, Phys. Rev. A 31 (1985), 1039-1045.
16. R. Livi, M. Pettini, S. Ruffo and A. Vulpiani, Further results on the equipartition threshold in large nonlinear Hamiltonian systems, Phys. Rev. A 31 (1985), 2740-2742.
17. S. Isola, R. Livi, S. Ruffo and A. Vulpiani, Stability and chaos in Hamiltonian dynamics, Phys. Rev A 33 (1986), 1163-1170.
18. R. Livi, M. Pettini, S. Ruffo and A. Vulpiani, Chaotic behaviour in nonlinear Hamiltonian systems and equilibrium statistical mechanics, J. Stat. Phys. 48 (1987), 539-559.
19. M. Pettini and M. Landolfi Relaxation properties and ergodicity breaking in nonlinear Hamiltonian dynamics, Phys. Rev A 41 (1990), 768-783.
20. M. Pettini and M. Cerruti-Sola, Strong stochasticity threshold in nonlinear Hamiltonian systems: effect of mixing times, Phys. Rev A 44 (1991), 975-987.