메뉴 건너뛰기




Volumn 337, Issue 3, 2000, Pages 237-341

Geometric approach to Hamiltonian dynamics and statistical mechanics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0346044201     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(00)00069-7     Document Type: Review
Times cited : (250)

References (158)
  • 3
    • 0037618855 scopus 로고
    • E. Fermi, Nuovo Cimento 25 (1923) 267. E. Fermi, Nuovo Cimento 26 (1923) 105.
    • (1923) Nuovo Cimento , vol.25 , pp. 267
    • Fermi, E.1
  • 4
    • 0043078472 scopus 로고
    • E. Fermi, Nuovo Cimento 25 (1923) 267. E. Fermi, Nuovo Cimento 26 (1923) 105.
    • (1923) Nuovo Cimento , vol.26 , pp. 105
    • Fermi, E.1
  • 5
    • 0001246972 scopus 로고
    • A.N. Kol'mogorov, Dokl. Akad. Nauk. SSSR 98 (1954) 527; V.I. Arnol'd, Russ. Math. Surv. 18 (1963) 9; J. M oser, Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. 2 1 (1962) 1; see also Refs. [2,57].
    • (1954) Dokl. Akad. Nauk. SSSR , vol.98 , pp. 527
    • Kol'mogorov, A.N.1
  • 6
    • 0002764805 scopus 로고
    • A.N. Kol'mogorov, Dokl. Akad. Nauk. SSSR 98 (1954) 527; V.I. Arnol'd, Russ. Math. Surv. 18 (1963) 9; J. M oser, Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. 2 1 (1962) 1; see also Refs. [2,57].
    • (1963) Russ. Math. Surv. , vol.18 , pp. 9
    • Arnol'd, V.I.1
  • 7
    • 0001851184 scopus 로고
    • see also Refs. [2,57]
    • A.N. Kol'mogorov, Dokl. Akad. Nauk. SSSR 98 (1954) 527; V.I. Arnol'd, Russ. Math. Surv. 18 (1963) 9; J. M oser, Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. 2 1 (1962) 1; see also Refs. [2,57].
    • (1962) Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. , vol.2 , Issue.1 , pp. 1
    • Oser, J.M.1
  • 9
    • 0002998341 scopus 로고
    • J. Hadamard, J. Math. Pures Appl. 4 (1898) 27; G.A. Hedlund, Bull. Am. Math. Soc. 45 (1939) 241; E. Hopf, Proc. Natl. Acad. Sci. 18 (1932) 263.
    • (1898) J. Math. Pures Appl. , vol.4 , pp. 27
    • Hadamard, J.1
  • 10
    • 0001585656 scopus 로고
    • J. Hadamard, J. Math. Pures Appl. 4 (1898) 27; G.A. Hedlund, Bull. Am. Math. Soc. 45 (1939) 241; E. Hopf, Proc. Natl. Acad. Sci. 18 (1932) 263.
    • (1939) Bull. Am. Math. Soc. , vol.45 , pp. 241
    • Hedlund, G.A.1
  • 11
    • 0002286325 scopus 로고
    • J. Hadamard, J. Math. Pures Appl. 4 (1898) 27; G.A. Hedlund, Bull. Am. Math. Soc. 45 (1939) 241; E. Hopf, Proc. Natl. Acad. Sci. 18 (1932) 263.
    • (1932) Proc. Natl. Acad. Sci. , vol.18 , pp. 263
    • Hopf, E.1
  • 14
    • 0001200214 scopus 로고
    • see also Ref. [7]
    • Ya.G. Sinai, Sov. Math. Dokl. 4 (1963) 1818; see also Ref. [7].
    • (1963) Sov. Math. Dokl. , vol.4 , pp. 1818
    • Sinai, Ya.G.1
  • 25
    • 5544294701 scopus 로고
    • H.E. Kandrup, Astrophys. J. 364 (1990) 420; Physica A 169 (1990) 73; Phys. Rev. E 56 (1997) 2722.
    • (1990) Astrophys. J. , vol.364 , pp. 420
    • Kandrup, H.E.1
  • 26
    • 5544294701 scopus 로고
    • H.E. Kandrup, Astrophys. J. 364 (1990) 420; Physica A 169 (1990) 73; Phys. Rev. E 56 (1997) 2722.
    • (1990) Physica A , vol.169 , pp. 73
  • 27
    • 0031221414 scopus 로고    scopus 로고
    • H.E. Kandrup, Astrophys. J. 364 (1990) 420; Physica A 169 (1990) 73; Phys. Rev. E 56 (1997) 2722.
    • (1997) Phys. Rev. E , vol.56 , pp. 2722
  • 28
    • 0003530085 scopus 로고    scopus 로고
    • Introduction to the Los Alamos Report LA-1940
    • E. Segré (Ed.), University of Chicago, Chicago
    • S. Ulam, Introduction to the Los Alamos Report LA-1940, in: E. Segré (Ed.), Collected Papers of Enrico Fermi, Vol. 2, University of Chicago, Chicago, 1965, p. 978.
    • (1965) Collected Papers of Enrico Fermi , vol.2 , pp. 978
    • Ulam, S.1
  • 30
    • 0346724810 scopus 로고
    • Laurea Thesis, Università di Firenze, unpublished
    • L. Casetti, Laurea Thesis, Università di Firenze, 1993, unpublished.
    • (1993)
    • Casetti, L.1
  • 35
    • 0346724809 scopus 로고
    • Laurea Thesis, Università di Firenze, unpublished
    • C. Clementi, Laurea Thesis, Università di Firenze, 1995, unpublished.
    • (1995)
    • Clementi, C.1
  • 36
    • 0346094184 scopus 로고
    • Laurea Thesis, Università di Firenze, unpublished
    • L. Caiani, Laurea Thesis, Università di Firenze, 1995, unpublished.
    • (1995)
    • Caiani, L.1
  • 48
    • 0038294367 scopus 로고    scopus 로고
    • P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1499; P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1543; P. Cipriani, M. Di Bari, Phys. Rev. Lett. 81 (1998) 5532; M. Di Bari, D. Boccaletti, P. Cipriani, G. Pucacco, Phys. Rev. E 55 (1997) 6448; P. Cipriani, G. Pucacco, Nuovo Cimento B 109 (1994) 325.
    • (1998) Planetary Space Sci. , vol.46 , pp. 1499
    • Cipriani, P.1    Di Bari, M.2
  • 49
    • 0042027189 scopus 로고    scopus 로고
    • P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1499; P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1543; P. Cipriani, M. Di Bari, Phys. Rev. Lett. 81 (1998) 5532; M. Di Bari, D. Boccaletti, P. Cipriani, G. Pucacco, Phys. Rev. E 55 (1997) 6448; P. Cipriani, G. Pucacco, Nuovo Cimento B 109 (1994) 325.
    • (1998) Planetary Space Sci. , vol.46 , pp. 1543
    • Cipriani, P.1    Di Bari, M.2
  • 50
    • 4243089421 scopus 로고    scopus 로고
    • P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1499; P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1543; P. Cipriani, M. Di Bari, Phys. Rev. Lett. 81 (1998) 5532; M. Di Bari, D. Boccaletti, P. Cipriani, G. Pucacco, Phys. Rev. E 55 (1997) 6448; P. Cipriani, G. Pucacco, Nuovo Cimento B 109 (1994) 325.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 5532
    • Cipriani, P.1    Di Bari, M.2
  • 51
    • 0008160582 scopus 로고    scopus 로고
    • P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1499; P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1543; P. Cipriani, M. Di Bari, Phys. Rev. Lett. 81 (1998) 5532; M. Di Bari, D. Boccaletti, P. Cipriani, G. Pucacco, Phys. Rev. E 55 (1997) 6448; P. Cipriani, G. Pucacco, Nuovo Cimento B 109 (1994) 325.
    • (1997) Phys. Rev. E , vol.55 , pp. 6448
    • Di Bari, M.1    Boccaletti, D.2    Cipriani, P.3    Pucacco, G.4
  • 52
    • 51249167205 scopus 로고
    • P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1499; P. Cipriani, M. Di Bari, Planetary Space Sci. 46 (1998) 1543; P. Cipriani, M. Di Bari, Phys. Rev. Lett. 81 (1998) 5532; M. Di Bari, D. Boccaletti, P. Cipriani, G. Pucacco, Phys. Rev. E 55 (1997) 6448; P. Cipriani, G. Pucacco, Nuovo Cimento B 109 (1994) 325.
    • (1994) Nuovo Cimento B , vol.109 , pp. 325
    • Cipriani, P.1    Pucacco, G.2
  • 54
    • 0037531043 scopus 로고
    • S.A. Rice, K.F. Freed, J.C. Light (Eds.), University of Chicago Press, Chicago
    • R. Thom, in: S.A. Rice, K.F. Freed, J.C. Light (Eds.), Statistical Mechanics, University of Chicago Press, Chicago, 1972, p. 93.
    • (1972) Statistical Mechanics , pp. 93
    • Thom, R.1
  • 55
    • 0003428398 scopus 로고
    • Pitman Press, London, and references therein quoted
    • More on phase transitions and Catastrophe theory can be found, in: T. Poston, I. Stewart (Eds.), Catastrophe Theory and its Applications, Pitman Press, London, 1978, and references therein quoted.
    • (1978) Catastrophe Theory and Its Applications
    • Poston, T.1    Stewart, I.2
  • 56
    • 17944364908 scopus 로고
    • Topological concepts in the theory of phase transitions
    • H.D. Döbner (Ed.), Springer, New York
    • M. Rasetti, Topological concepts in the theory of phase transitions, in: H.D. Döbner (Ed.), Differential Geometric Methods in Mathematical Physics, Springer, New York, 1979; in: W. Güttinger (Ed.), Structural Stability in Statistical Mechanics, Springer Tracts in Math., Springer, New York, 1979.
    • (1979) Differential Geometric Methods in Mathematical Physics
    • Rasetti, M.1
  • 57
    • 9744240456 scopus 로고
    • Springer Tracts in Math., Springer, New York
    • M. Rasetti, Topological concepts in the theory of phase transitions, in: H.D. Döbner (Ed.), Differential Geometric Methods in Mathematical Physics, Springer, New York, 1979; in: W. Güttinger (Ed.), Structural Stability in Statistical Mechanics, Springer Tracts in Math., Springer, New York, 1979.
    • (1979) Structural Stability in Statistical Mechanics
    • Güttinger, W.1
  • 59
    • 85037475252 scopus 로고    scopus 로고
    • cond-mat/9911257 and references therein quoted
    • D.H.E. Gross, E. Votyakov, cond-mat/9911257 and references therein quoted.
    • Gross, D.H.E.1    Votyakov, E.2
  • 60
  • 61
    • 0001112302 scopus 로고    scopus 로고
    • H.H. Rugh, Phys. Rev. Lett. 78 (1997) 772; J. Phys. A 31 (1998) 7761.
    • (1998) J. Phys. A , vol.31 , pp. 7761
  • 79
    • 17044421499 scopus 로고
    • G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74 (1995) 2694; J. Stat. Phys. 80 (1995) 931.
    • (1995) J. Stat. Phys. , vol.80 , pp. 931
  • 83
    • 0003530085 scopus 로고    scopus 로고
    • E. Fermi, J. Pasta, S. Ulam (with M. Tsingou), Los Alamos Report LA-1940, D.C. Mattis (Ed.), The Many-Body Problem, World Scientific, Singapore, 1992, and also in: E. Segré (Ed.), Collected Papers of Enrico Fermi, Vol. 2, University of Chicago, Chicago, 1965, p. 978.
    • Los Alamos Report LA-1940
    • Fermi, E.1    Pasta, J.2    Ulam, S.3    Tsingou, M.4
  • 84
    • 85037462479 scopus 로고
    • Singapore
    • E. Fermi, J. Pasta, S. Ulam (with M. Tsingou), Los Alamos Report LA-1940, D.C. Mattis (Ed.), The Many-Body Problem, World Scientific, Singapore, 1992, and also in: E. Segré (Ed.), Collected Papers of Enrico Fermi, Vol. 2, University of Chicago, Chicago, 1965, p. 978.
    • (1992) The Many-Body Problem, World Scientific
  • 85
    • 0008124548 scopus 로고
    • University of Chicago, Chicago
    • E. Fermi, J. Pasta, S. Ulam (with M. Tsingou), Los Alamos Report LA-1940, D.C. Mattis (Ed.), The Many-Body Problem, World Scientific, Singapore, 1992, and also in: E. Segré (Ed.), Collected Papers of Enrico Fermi, Vol. 2, University of Chicago, Chicago, 1965, p. 978.
    • (1965) Collected Papers of Enrico Fermi , vol.2 , pp. 978
    • Segré, E.1
  • 95
    • 36149023450 scopus 로고
    • Rigorous results about the appearance of these singularities have been given in: C.N Yang, T.D. Lee, Phys. Rev. 87 (1952) 404, as far as the grand-canonical ensemble is concerned, and in: D. Ruelle, Thermodynamic Formalism, Encyclopaedia of Mathematics and its Applications, Addison-Wesley, New York, 1978, as far as the canonical ensemble is concerned.
    • (1952) Phys. Rev. , vol.87 , pp. 404
    • Yang, C.N.1    Lee, T.D.2
  • 96
    • 0003838766 scopus 로고
    • Addison-Wesley, New York, as far as the canonical ensemble is concerned
    • Rigorous results about the appearance of these singularities have been given in: C.N Yang, T.D. Lee, Phys. Rev. 87 (1952) 404, as far as the grand-canonical ensemble is concerned, and in: D. Ruelle, Thermodynamic Formalism, Encyclopaedia of Mathematics and its Applications, Addison-Wesley, New York, 1978, as far as the canonical ensemble is concerned.
    • (1978) Thermodynamic Formalism, Encyclopaedia of Mathematics and Its Applications
    • Ruelle, D.1
  • 97
    • 0032393880 scopus 로고    scopus 로고
    • C. Domb, M.S. Green (Eds.), Academic Press, London
    • M.E. Fisher, D. Jasnow, in: C. Domb, M.S. Green (Eds.), Phase Transitions and Critical Phenomena, Vol. 4, Academic Press, London, 1976; M.E. Fisher, Rev. Mod. Phys. 70 (1998) 653.
    • (1976) Phase Transitions and Critical Phenomena , vol.4
    • Fisher, M.E.1    Jasnow, D.2
  • 98
    • 0032393880 scopus 로고    scopus 로고
    • M.E. Fisher, D. Jasnow, in: C. Domb, M.S. Green (Eds.), Phase Transitions and Critical Phenomena, Vol. 4, Academic Press, London, 1976; M.E. Fisher, Rev. Mod. Phys. 70 (1998) 653.
    • (1998) Rev. Mod. Phys. , vol.70 , pp. 653
    • Fisher, M.E.1
  • 127
  • 130
    • 0040495626 scopus 로고
    • To solve Eqs. (135) for a general (i.e., not mean-field-like) potential energy function one could borrow methods from: J. Vollmer, W. Breymann, R. Schilling, Phys. Rev. B 47 (1993) 11767.
    • (1993) Phys. Rev. B , vol.47 , pp. 11767
    • Vollmer, J.1    Breymann, W.2    Schilling, R.3
  • 133
    • 25344432551 scopus 로고
    • A. Dhar, Physica A 259 (1989) 119.
    • (1989) Physica A , vol.259 , pp. 119
    • Dhar, A.1
  • 138
    • 0004057466 scopus 로고
    • The University of Chicago Press, Chicago
    • R.M. Wald, General Relativity, The University of Chicago Press, Chicago, 1984.
    • (1984) General Relativity
    • Wald, R.M.1
  • 142
    • 0003288058 scopus 로고
    • Critical Point Theory and Submanifold Geometry
    • Springer, Berlin
    • R.S. Palais, C. Terng, Critical Point Theory and Submanifold Geometry, Lecture Notes on Mathematics, Vol. 1353, Springer, Berlin, 1988.
    • (1988) Lecture Notes on Mathematics , vol.1353
    • Palais, R.S.1    Terng, C.2
  • 146
  • 149
    • 0002356196 scopus 로고
    • also reprinted in [128]
    • V.I. Arnol'd, Russ. Math. Surv. 18 (1964) 85, also reprinted in [128].
    • (1964) Russ. Math. Surv. , vol.18 , pp. 85
    • Arnol'd, V.I.1
  • 154
    • 85037474639 scopus 로고
    • Lyapunov spectra and characterization of chaotic dynamics
    • R. Livi, J.-P. Nadal (Eds.), Nova Publishing
    • S. Ruffo, Lyapunov spectra and characterization of chaotic dynamics, in: R. Livi, J.-P. Nadal (Eds.), Complex Dynamics, Nova Publishing, 1994.
    • (1994) Complex Dynamics
    • Ruffo, S.1
  • 156
    • 0347985552 scopus 로고
    • R. Livi, A. Politi, S. Ruffo, J. Stat. Phys. 19 (1986) 2083; Ch. Dellago, L. Glotz, H.A. Posch, Phys. Rev. E 52 (1995) 4817; see also Ref. [92].
    • (1986) J. Stat. Phys. , vol.19 , pp. 2083
    • Livi, R.1    Politi, A.2    Ruffo, S.3
  • 157
    • 0000066276 scopus 로고
    • see also Ref. [92]
    • R. Livi, A. Politi, S. Ruffo, J. Stat. Phys. 19 (1986) 2083; Ch. Dellago, L. Glotz, H.A. Posch, Phys. Rev. E 52 (1995) 4817; see also Ref. [92].
    • (1995) Phys. Rev. E , vol.52 , pp. 4817
    • Dellago, Ch.1    Glotz, L.2    Posch, H.A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.