Approach to equilibrium in a chain of nonlinear oscillators
J. Phys. France, 43 5 (1982) 707-713
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https://doi.org/10.1063/1.1861264
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https://doi.org/10.1016/j.physleta.2003.11.052
Chance in Physics
Stefano RuffoLecture Notes in Physics, Chance in Physics 574 243 (2001)
https://doi.org/10.1007/3-540-44966-3_18
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Dario BambusiNonlinearity 12 (4) 823 (1999)
https://doi.org/10.1088/0951-7715/12/4/305
Exact solutions in the FPU oscillator chain
P. Poggi and S. RuffoPhysica D: Nonlinear Phenomena 103 (1-4) 251 (1997)
https://doi.org/10.1016/S0167-2789(96)00262-X
On the approach to equilibrium of a Hamiltonian chain of anharmonic oscillators
G ParisiEurophysics Letters (EPL) 40 (4) 357 (1997)
https://doi.org/10.1209/epl/i1997-00471-9
Intermittency in nonlinear stochastic systems
L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta and S. SantucciPhysics Letters A 156 (1-2) 37 (1991)
https://doi.org/10.1016/0375-9601(91)90123-P
Two energy conserving numerical schemes for the Sine-Gordon equation
Zhang Fei and Luis VázquezApplied Mathematics and Computation 45 (1) 17 (1991)
https://doi.org/10.1016/0096-3003(91)90087-4
Analysis of Four Numerical Schemes for a Nonlinear Klein-Gordon Equation
Salvador Jiménez and Luis VázquezApplied Mathematics and Computation 35 (1) 61 (1990)
https://doi.org/10.1016/0096-3003(90)90091-G
A numerical study of chaos in the one-dimensionalphi4model
Douglas A Bradley-Hutchison and Harvey K ShepardPhysica Scripta 40 (6) 731 (1989)
https://doi.org/10.1088/0031-8949/40/6/005
Nonlinear Evolution and Chaotic Phenomena
Luigi GalganiNATO ASI Series, Nonlinear Evolution and Chaotic Phenomena 176 147 (1988)
https://doi.org/10.1007/978-1-4613-1017-4_10
The ultraviolet problem and analytical properties of classical field theories
R Livi, M Pettini, S Ruffo and A VulpianiJournal of Physics A: Mathematical and General 20 (3) 577 (1987)
https://doi.org/10.1088/0305-4470/20/3/019
Stochastic Processes in Classical and Quantum Systems
Luigi GalganiLecture Notes in Physics, Stochastic Processes in Classical and Quantum Systems 262 269 (1986)
https://doi.org/10.1007/3540171665_70
Equipartition threshold in nonlinear large Hamiltonian systems: The Fermi-Pasta-Ulam model
Roberto Livi, Marco Pettini, Stefano Ruffo, Massimo Sparpaglione and Angelo VulpianiPhysical Review A 31 (2) 1039 (1985)
https://doi.org/10.1103/PhysRevA.31.1039
Short-time asymptotics in classical nonlinear wave equations
R. Livi, S. Ruffo, M. Pettini and A. VulpianiIl Nuovo Cimento B Series 11 89 (2) 120 (1985)
https://doi.org/10.1007/BF02723541
Chaos in Astrophysics
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https://doi.org/10.1007/978-94-009-5468-7_9
Chaos and Statistical Methods
U. FrischSpringer Series in Synergetics, Chaos and Statistical Methods 24 211 (1984)
https://doi.org/10.1007/978-3-642-69559-9_29
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Giancarlo Benettin, Luigi Galgani and Antonio GiorgilliNature 311 (5985) 444 (1984)
https://doi.org/10.1038/311444a0
Pole condensation and the Riemann surface associated with a shock in Burgers' equation
D. Bessis and J.D. FournierJournal de Physique Lettres 45 (17) 833 (1984)
https://doi.org/10.1051/jphyslet:019840045017083300
Complex poles, spatial intermittencies, and energy transfer in a classical nonlinear string
B. Bassetti, P. Butera, M. Raciti and M. SparpaglionePhysical Review A 30 (2) 1033 (1984)
https://doi.org/10.1103/PhysRevA.30.1033
Ordered and stochastic behavior in a two-dimensional Lennard-Jones system
Giancarlo Benettin and Alexander TenenbaumPhysical Review A 28 (5) 3020 (1983)
https://doi.org/10.1103/PhysRevA.28.3020
Relaxation to different stationary states in the Fermi-Pasta-Ulam model
Roberto Livi, Marco Pettini, Stefano Ruffo, Massimo Sparpaglione and Angelo VulpianiPhysical Review A 28 (6) 3544 (1983)
https://doi.org/10.1103/PhysRevA.28.3544
Relaxation time and randomness in phase space
M. CasartelliIl Nuovo Cimento B Series 11 76 (2) 97 (1983)
https://doi.org/10.1007/BF02721546
Numerical computations of Liapunov exponents for a discretized one-dimensional nonlinear Klein-Gordon equation
G. Caravati, A. Giorgilli and L. GalganiLettere al Nuovo Cimento 38 (11) 385 (1983)
https://doi.org/10.1007/BF02789596
Approach to equilibrium in a lattice field theory
F. Marchesoni and M. SparpaglioneIl Nuovo Cimento B 69 (2) 283 (1982)
https://doi.org/10.1007/BF02721272