메뉴 건너뛰기




Volumn 5, Issue 4, 2005, Pages 991-1004

Local chaotic behaviour in the Fermi-Pasta-Ulam system

Author keywords

FPU model; Nonlinear chain; Thermodynamic limit

Indexed keywords


EID: 28444449084     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2005.5.991     Document Type: Article
Times cited : (20)

References (29)
  • 1
    • 0018989294 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them, part 1: Theory
    • G. Benettin, L. Galgani, A. Giorgilli, and J.-M. Strelcyn, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them, part 1: theory, Meccanica, pages 9-20, 1980.
    • (1980) Meccanica , pp. 9-20
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.-M.4
  • 2
    • 0018992908 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them, part 2: Numerical applications
    • G. Benettin, L. Galgani, A. Giorgilli, and J.-M. Strelcyn, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them, part 2: numerical applications, Meccanica, pages 21-30, 1980.
    • (1980) Meccanica , pp. 21-30
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.-M.4
  • 3
    • 21344491735 scopus 로고
    • On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms
    • G. Benettin and A. Giorgilli, On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms, J. Statist. Phys., 74 (1994), 1117-1143.
    • (1994) J. Statist. Phys. , vol.74 , pp. 1117-1143
    • Benettin, G.1    Giorgilli, A.2
  • 5
    • 1042301145 scopus 로고    scopus 로고
    • Exponentially long times to equipartition in the thermodynamic limit
    • L. Berchialla, A. Giorgilli, and S. Paleari. Exponentially long times to equipartition in the thermodynamic limit, Phys. Lett. A, 321 (2004), 167-172.
    • (2004) Phys. Lett. A , vol.321 , pp. 167-172
    • Berchialla, L.1    Giorgilli, A.2    Paleari, S.3
  • 6
    • 0009066252 scopus 로고
    • Anharmonic chain with Lennard-Jones interaction
    • P. Bocchieri, A. Scotti, B. Bearzi, and A. Loinger, Anharmonic chain with Lennard-Jones interaction, Phys. Rev. A, 2 (1970), 2013-2019.
    • (1970) Phys. Rev. A , vol.2 , pp. 2013-2019
    • Bocchieri, P.1    Scotti, A.2    Bearzi, B.3    Loinger, A.4
  • 7
    • 27944489195 scopus 로고    scopus 로고
    • On diffusion in high-dimensional Hamiltonian systems
    • in press
    • J. Bourgain and V. Kaloshin, On diffusion in high-dimensional Hamiltonian systems, J. Funct. Anal., 2005. in press.
    • (2005) J. Funct. Anal.
    • Bourgain, J.1    Kaloshin, V.2
  • 8
    • 0000313054 scopus 로고    scopus 로고
    • The Fermi-Pasta-Ulam problem revisited: Stochasticity thresholds in nonlinear Hamiltonian systems
    • 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 (3), 55 (6, part A), (1997), 6566-6574.
    • (1997) Phys. Rev. E (3) , vol.55 , Issue.6 PART A , pp. 6566-6574
    • Casetti, L.1    Cerruti-Sola, M.2    Pettini, M.3    Cohen, E.G.D.4
  • 9
    • 0001586081 scopus 로고
    • On the number of isolating integrals in Hamiltonian systems
    • G. Countopoulos, L. Galgani, and A. Giorgilli, On the number of isolating integrals in Hamiltonian systems, Phys. Rev. A, 18 (1978), 1183-1189.
    • (1978) Phys. Rev. A , vol.18 , pp. 1183-1189
    • Countopoulos, G.1    Galgani, L.2    Giorgilli, A.3
  • 10
    • 0342792866 scopus 로고
    • Time scale to ergodicity in the Fermi-Pasta-Ulam system
    • J. De Luca, A. Lichtenberg, and M. A. Lieberman, Time scale to ergodicity in the Fermi-Pasta-Ulam system, Chaos, 5 (1995), 283-297.
    • (1995) Chaos , vol.5 , pp. 283-297
    • De Luca, J.1    Lichtenberg, A.2    Lieberman, M.A.3
  • 11
    • 0007716335 scopus 로고
    • Energy transition and time scale to equipartition in the Fermi-Pasta-Ulam oscillator chain
    • J. De Luca, A. Lichtenberg, and S. Ruffo, Energy transition and time scale to equipartition in the Fermi-Pasta-Ulam oscillator chain, Phys. Rev. E (3), 51 (1995), 2877-2884.
    • (1995) Phys. Rev. E (3) , vol.51 , pp. 2877-2884
    • De Luca, J.1    Lichtenberg, A.2    Ruffo, S.3
  • 12
    • 0009017942 scopus 로고    scopus 로고
    • Universal evolution to equipartition in oscillator chain
    • J. De Luca, A. Lichtenberg, and S. Ruffo, Universal evolution to equipartition in oscillator chain, Phys. Rev. E (3), 54 (1996), 2329-2333.
    • (1996) Phys. Rev. E (3) , vol.54 , pp. 2329-2333
    • De Luca, J.1    Lichtenberg, A.2    Ruffo, S.3
  • 13
    • 0000535935 scopus 로고    scopus 로고
    • Finite times to equipartition in the thermodynamic limit
    • J. De Luca, A. Lichtenberg, and S. Ruffo, Finite times to equipartition in the thermodynamic limit, Phys. Rev. E (3), 60 (1999), 3781-3786.
    • (1999) Phys. Rev. E (3) , vol.60 , pp. 3781-3786
    • De Luca, J.1    Lichtenberg, A.2    Ruffo, S.3
  • 16
    • 0001276861 scopus 로고
    • On the problem of energy equipartition for large systems of the Fermi-Pasta-Ulam type: Analytical and numerical estimates
    • 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, Phys. D, 59 (1992), 334-348.
    • (1992) Phys. D , vol.59 , pp. 334-348
    • Galgani, L.1    Giorgilli, A.2    Martinoli, A.3    Vanzini, S.4
  • 17
    • 6744248668 scopus 로고    scopus 로고
    • New mechanisms for lack of equipartion of energy
    • A. Haro and R. de la Llave, New mechanisms for lack of equipartion of energy, Phys. Rev. Lett., 89 (2000), 1859-1862.
    • (2000) Phys. Rev. Lett. , vol.89 , pp. 1859-1862
    • Haro, A.1    De La Llave, R.2
  • 18
    • 0002980692 scopus 로고
    • Statistical properties of a nonlinear string
    • F. M. Izrailev and B. V. Chirikov, Statistical properties of a nonlinear string, Sov. Phys. Dokl., 11 (1966), 30-32.
    • (1966) Sov. Phys. Dokl. , vol.11 , pp. 30-32
    • Izrailev, F.M.1    Chirikov, B.V.2
  • 19
    • 0002980692 scopus 로고
    • Stochasticity of the simplest dynamical model with divided phase space
    • F. M. Izrailev and B. V. Chirikov, Stochasticity of the simplest dynamical model with divided phase space, Sov. Phys. Dokl., 11 (1966), 30.
    • (1966) Sov. Phys. Dokl. , vol.11 , pp. 30
    • Izrailev, F.M.1    Chirikov, B.V.2
  • 20
    • 0013087334 scopus 로고
    • Vanishing stability thresholds in the thermodynamic limit of nonintegrable conservative systems
    • H. Kantz, Vanishing stability thresholds in the thermodynamic limit of nonintegrable conservative systems, Phys. D, 39 (2-3) (1989), 322-335.
    • (1989) Phys. D , vol.39 , Issue.2-3 , pp. 322-335
    • Kantz, H.1
  • 21
    • 0347583689 scopus 로고
    • Equipartition thresholds in chains of anharmonic oscillators
    • H. Kantz, R. Livi, and S. Ruffo, Equipartition thresholds in chains of anharmonic oscillators, J. Statis. Phys., 76 (1994), 627-643.
    • (1994) J. Statis. Phys. , vol.76 , pp. 627-643
    • Kantz, H.1    Livi, R.2    Ruffo, S.3
  • 22
    • 0000701062 scopus 로고
    • Relaxation to different stationary states in the Fermi-Pasta-Ulam model
    • 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.
    • (1983) Phys. Rev. A , vol.28 , pp. 3544-3552
    • Livi, R.1    Pettini, M.2    Ruffo, S.3    Sparpaglione, M.4    Vulpiani, A.5
  • 23
    • 33646652279 scopus 로고
    • Equipartition threshold in nonlinear large Hamiltonian system: The Fermi-Pasta-Ulam model
    • R. Livi, M. Pettini, S. Ruffo, M. Sparpaglione, and A. Vulpiani, Equipartition threshold in nonlinear large Hamiltonian system: the Fermi-Pasta-Ulam model, Phys. Rev. A, 31 (1985), 1039-1045.
    • (1985) Phys. Rev. A , vol.31 , pp. 1039-1045
    • Livi, R.1    Pettini, M.2    Ruffo, S.3    Sparpaglione, M.4    Vulpiani, A.5
  • 24
    • 0002781295 scopus 로고
    • A note on an existence of conditionally periodic oscillation in a one-dimensional anharmonic lattice
    • T. Nishida, A note on an existence of conditionally periodic oscillation in a one-dimensional anharmonic lattice, Mem. Fac. Engrg. Kyoto Univ., 33 (1971), 27-34.
    • (1971) Mem. Fac. Engrg. Kyoto Univ. , vol.33 , pp. 27-34
    • Nishida, T.1
  • 25
    • 0038434713 scopus 로고
    • A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems
    • V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč., 19 (1968), 179-210.
    • (1968) Trudy Moskov. Mat. Obšč. , vol.19 , pp. 179-210
    • Oseledec, V.I.1
  • 26
    • 33748326391 scopus 로고    scopus 로고
    • Equipartition times in a Fermi-Pasta-Ulam system
    • Dynamical systems and differential equations (Pomona, CA, 2004)
    • S. Paleari and T. Penati, Equipartition times in a Fermi-Pasta-Ulam system, Discrete Contin. Dyn. Syst., (suppl.), 2005. Dynamical systems and differential equations (Pomona, CA, 2004).
    • (2005) Discrete Contin. Dyn. Syst. , Issue.SUPPL.
    • Paleari, S.1    Penati, T.2
  • 27
    • 0000569924 scopus 로고
    • Relaxation properties and ergodicity breaking in nonlinear Hamiltonian dynamics
    • M. Pettini and M. Landolfi, Relaxation properties and ergodicity breaking in nonlinear Hamiltonian dynamics, Phys. Rev. A (3), 41 (1990) 768-783.
    • (1990) Phys. Rev. A (3) , vol.41 , pp. 768-783
    • Pettini, M.1    Landolfi, M.2
  • 28
    • 0035531312 scopus 로고    scopus 로고
    • Symmetry and resonance in periodic FPU chains
    • B. Rink, Symmetry and resonance in periodic FPU chains, Comm. Math. Phys., 218 (2001), 665-685.
    • (2001) Comm. Math. Phys. , vol.218 , pp. 665-685
    • Rink, B.1
  • 29
    • 0000931034 scopus 로고    scopus 로고
    • Energy equipartition starting from high-frequency modes in the Fermi-Pasta-Ulam β oscillator chain
    • K. Ullmann, A. Lichtenberg, and G. Corso, Energy equipartition starting from high-frequency modes in the Fermi-Pasta-Ulam β oscillator chain, Phys. Rev. E (3), 61 (2000), 2471-2477.
    • (2000) Phys. Rev. E (3) , vol.61 , pp. 2471-2477
    • Ullmann, K.1    Lichtenberg, A.2    Corso, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.