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Volumn 12, Issue SUPPL. 1, 2005, Pages 212-227

Explicit integration of the Hénon-Heiles Hamiltonians

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EID: 27844565225     PISSN: 14029251     EISSN: 14029251     Source Type: Journal    
DOI: 10.2991/jnmp.2005.12.s1.18     Document Type: Article
Times cited : (37)

References (51)
  • 1
    • 0039347964 scopus 로고    scopus 로고
    • On the weak Kowalevski-Painlevé property for hyperelliptically separable systems
    • S. Abenda and Yu. Fedorov, On the weak Kowalevski-Painlevé property for hyperelliptically separable systems, Acta Appl. Math. 60 (2000) 137-178.
    • (2000) Acta Appl. Math. , vol.60 , pp. 137-178
    • Abenda, S.1    Fedorov, Yu.2
  • 2
    • 0040911334 scopus 로고
    • The complete Whittaker theorem for two-dimensional integrable systems and its application
    • A. Ankiewicz and C. Pask, The complete Whittaker theorem for two-dimensional integrable systems and its application, J. Phys. A 16 (1983) 4203-4208.
    • (1983) J. Phys. A , vol.16 , pp. 4203-4208
    • Ankiewicz, A.1    Pask, C.2
  • 4
    • 0001530153 scopus 로고
    • Hamiltonian structures and Lax equations
    • O. Babelon and C.-M. Viallet, Hamiltonian structures and Lax equations, Phys. Lett. B 237 (1990) 411-416.
    • (1990) Phys. Lett. B , vol.237 , pp. 411-416
    • Babelon, O.1    Viallet, C.-M.2
  • 6
    • 0001146110 scopus 로고
    • Integrable quartic potentials and coupled KdV equations
    • S. Baker, V. Z. Enol'skii and A. P. Fordy, Integrable quartic potentials and coupled KdV equations, Phys. Lett. A 201 (1995) 167-174.
    • (1995) Phys. Lett. A , vol.201 , pp. 167-174
    • Baker, S.1    Enol'skii, V.Z.2    Fordy, A.P.3
  • 7
    • 21344480811 scopus 로고
    • A generalized Hénon-Heiles system and related integrable Newton equations
    • M. Blaszak and S. Rauch-Wojciechowski, A generalized Hénon-Heiles system and related integrable Newton equations, J. Math. Phys. 35 (1994) 1693-1709.
    • (1994) J. Math. Phys. , vol.35 , pp. 1693-1709
    • Blaszak, M.1    Rauch-Wojciechowski, S.2
  • 8
    • 0000972235 scopus 로고
    • Integrable Hamiltonian systems and the Painlevé property
    • T. Bountis, H. Segur and F. Vivaldi, Integrable Hamiltonian systems and the Painlevé property, Phys. Rev. A 25 (1982) 1257-1264.
    • (1982) Phys. Rev. A , vol.25 , pp. 1257-1264
    • Bountis, T.1    Segur, H.2    Vivaldi, F.3
  • 9
    • 0039135631 scopus 로고
    • Differential equations with fixed critical points
    • F. J. Bureau, Differential equations with fixed critical points, Annali di Matematica pura ed applicata LXVI (1964) 1-116.
    • (1964) Annali di Matematica Pura Ed Applicata , vol.66 , pp. 1-116
    • Bureau, F.J.1
  • 10
    • 36749106140 scopus 로고
    • Analytic structure of the Hénon-Heiles Hamiltonian in integrable and nonintegrable regimes
    • Chang Y. F., M. Tabor and J. Weiss, Analytic structure of the Hénon-Heiles Hamiltonian in integrable and nonintegrable regimes, J. Math. Phys. 23 (1982) 531-538.
    • (1982) J. Math. Phys. , vol.23 , pp. 531-538
    • Chang, Y.F.1    Tabor, M.2    Weiss, J.3
  • 11
    • 0042173311 scopus 로고
    • Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes
    • J. Chazy, Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes, Acta Math. 34 (1911) 317-385.
    • (1911) Acta Math. , vol.34 , pp. 317-385
    • Chazy, J.1
  • 12
    • 0001050990 scopus 로고    scopus 로고
    • The Painlevé approach to nonlinear ordinary differential equations
    • The Painlevé property, one century later, ed. R. Conte (Springer, New York). Solv-int/9710020
    • R. Conte, The Painlevé approach to nonlinear ordinary differential equations, The Painlevé property, one century later, 77-180, ed. R. Conte, CRM Series in Mathematical Physics (Springer, New York, 1999). Solv-int/9710020.
    • (1999) CRM Series in Mathematical Physics , pp. 77-180
    • Conte, R.1
  • 13
    • 43949163853 scopus 로고
    • A perturbative Painlevé approach to nonlinear differential equations
    • R. Conte, A. P. Fordy and A. Pickering, A perturbative Painlevé approach to nonlinear differential equations, Physica D 69 (1993) 33-58.
    • (1993) Physica D , vol.69 , pp. 33-58
    • Conte, R.1    Fordy, A.P.2    Pickering, A.3
  • 14
    • 30444448758 scopus 로고    scopus 로고
    • Completeness of the Hénon-Heiles Hamiltonians
    • Théories asymptotiques et équations de Painlevé, eds. E. Delabaere and M. Loday (SMF, Paris)
    • R. Conte, M. Musette and C. Verhoeven, Completeness of the Hénon-Heiles Hamiltonians, Théories asymptotiques et équations de Painlevé, eds. E. Delabaere and M. Loday, Séminaires et congrès (SMF, Paris, 2005).
    • (2005) Séminaires et Congrès
    • Conte, R.1    Musette, M.2    Verhoeven, C.3
  • 15
    • 23044454168 scopus 로고    scopus 로고
    • Completeness of the cubic and quartic Hénon-Heiles Hamiltonians
    • submitted
    • R. Conte, M. Musette and C. Verhoeven, Completeness of the cubic and quartic Hénon-Heiles Hamiltonians, Theor. Math. Phys. submitted (2005).
    • (2005) Theor. Math. Phys.
    • Conte, R.1    Musette, M.2    Verhoeven, C.3
  • 17
    • 0000424311 scopus 로고    scopus 로고
    • Higher order Painlevé equations in the polynomial class, I. Bureau symbol P2
    • C. M. Cosgrove, Higher order Painlevé equations in the polynomial class, I. Bureau symbol P2, Stud. Appl. Math. 104 (2000) 1-65.
    • (2000) Stud. Appl. Math. , vol.104 , pp. 1-65
    • Cosgrove, C.M.1
  • 20
    • 0000309420 scopus 로고
    • Equations of Korteweg-de Vries type and simple Lie Algebras
    • V. G. Drinfel'd and V. V. Sokolov, Equations of Korteweg-de Vries type and simple Lie Algebras, Soviet Math. Dokl. 23 (1981) 457-462.
    • (1981) Soviet Math. Dokl. , vol.23 , pp. 457-462
    • Drinfel'd, V.G.1    Sokolov, V.V.2
  • 22
    • 34250120087 scopus 로고
    • English
    • [English: Journal of Soviet. Math. 30 (1985) 1975-2036].
    • (1985) Journal of Soviet. Math. , vol.30 , pp. 1975-2036
  • 24
    • 44949270946 scopus 로고
    • The Hénon-Heiles system revisited
    • A. P. Fordy, The Hénon-Heiles system revisited, Physica D 52 (1991) 204-210.
    • (1991) Physica D , vol.52 , pp. 204-210
    • Fordy, A.P.1
  • 25
    • 0001471498 scopus 로고
    • Some remarkable nonlinear transformations
    • A. P. Fordy and J. Gibbons, Some remarkable nonlinear transformations, Phys. Lett. A 75 (1980) 325-325.
    • (1980) Phys. Lett. A , vol.75 , pp. 325-325
    • Fordy, A.P.1    Gibbons, J.2
  • 26
    • 0001565837 scopus 로고
    • Nonlinear Schrödinger equations and simple Lie algebras
    • A. P. Fordy and P. P. Kulish, Nonlinear Schrödinger equations and simple Lie algebras, Commun. Math. Phys. 89 (1983) 427-443.
    • (1983) Commun. Math. Phys. , vol.89 , pp. 427-443
    • Fordy, A.P.1    Kulish, P.P.2
  • 27
    • 34250588266 scopus 로고
    • Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est à points critiques fixes
    • B. Gambier, Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est à points critiques fixes, Acta Math. 33 (1910) 1-55.
    • (1910) Acta Math. , vol.33 , pp. 1-55
    • Gambier, B.1
  • 28
    • 0000040751 scopus 로고
    • Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
    • B. Grammaticos, B. Dorizzi and A. Ramani, Integrability of Hamiltonians with third- and fourth-degree polynomial potentials, J. Math. Phys. 24 (1983) 2289-2295.
    • (1983) J. Math. Phys. , vol.24 , pp. 2289-2295
    • Grammaticos, B.1    Dorizzi, B.2    Ramani, A.3
  • 29
    • 0002519122 scopus 로고
    • The applicability of the third integral of motion: Some numerical experiments
    • M. Hénon and C. Heiles, The applicability of the third integral of motion: some numerical experiments, Astron. J. 69 (1964) 73-79.
    • (1964) Astron. J. , vol.69 , pp. 73-79
    • Hénon, M.1    Heiles, C.2
  • 30
    • 36549092691 scopus 로고
    • Classical versus quantum integrability
    • J. Hietarinta, Classical versus quantum integrability, J. Math. Phys. 25 (1984) 1833-1840.
    • (1984) J. Math. Phys. , vol.25 , pp. 1833-1840
    • Hietarinta, J.1
  • 31
    • 0040215985 scopus 로고
    • Direct method for the search of the second invariant
    • J. Hietarinta, Direct method for the search of the second invariant, Phys. Rep. 147 (1987) 87-154.
    • (1987) Phys. Rep. , vol.147 , pp. 87-154
    • Hietarinta, J.1
  • 32
    • 85008279103 scopus 로고
    • Solitons and infinite dimensional Lie algebras
    • M. Jimbo and T. Miwa, Solitons and infinite dimensional Lie algebras, Publ. RIMS, Kyoto 19 (1983) 943-1001.
    • (1983) Publ. RIMS, Kyoto , vol.19 , pp. 943-1001
    • Jimbo, M.1    Miwa, T.2
  • 33
  • 34
    • 21344478358 scopus 로고
    • Caustics in 1+1 integrable systems
    • A. V. Kitaev, Caustics in 1+1 integrable systems, J. Math. Phys. 35 (1994) 2934-2954.
    • (1994) J. Math. Phys. , vol.35 , pp. 2934-2954
    • Kitaev, A.V.1
  • 35
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21 (1968) 467-490.
    • (1968) Comm. Pure Appl. Math. , vol.21 , pp. 467-490
    • Lax, P.D.1
  • 36
    • 4043172911 scopus 로고    scopus 로고
    • On CKP and BKP equations related to the generalized quartic Hénon-Heiles Hamiltonian
    • M. Musette and C. Verhoeven, On CKP and BKP equations related to the generalized quartic Hénon-Heiles Hamiltonian, Theor. Math. Phys. 137 (2003) 1561-1573.
    • (2003) Theor. Math. Phys. , vol.137 , pp. 1561-1573
    • Musette, M.1    Verhoeven, C.2
  • 39
    • 36449007692 scopus 로고
    • Separability and Lax pairs for Hénon-Heiles system
    • V. Ravoson, L. Gavrilov and R. Caboz, Separability and Lax pairs for Hénon-Heiles system, J. Math. Phys. 34 (1993) 2385-2393.
    • (1993) J. Math. Phys. , vol.34 , pp. 2385-2393
    • Ravoson, V.1    Gavrilov, L.2    Caboz, R.3
  • 40
    • 0039991208 scopus 로고
    • Generalized separability for a Hamiltonian with nonseparable quartic potential
    • V. Ravoson, A. Ramani and B. Grammaticos, Generalized separability for a Hamiltonian with nonseparable quartic potential, Phys. Letters A 191 (1994) 91-95.
    • (1994) Phys. Letters A , vol.191 , pp. 91-95
    • Ravoson, V.1    Ramani, A.2    Grammaticos, B.3
  • 41
    • 0039332536 scopus 로고
    • Canonical transformation between integrable Hénon-Heiles systems
    • M. Salerno, V. Z. Enol'skii and D. V. Leykin, Canonical transformation between integrable Hénon-Heiles systems, Phys. Rev. E 49 (1994) 5897-5899.
    • (1994) Phys. Rev. E , vol.49 , pp. 5897-5899
    • Salerno, M.1    Enol'skii, V.Z.2    Leykin, D.V.3
  • 42
    • 0039359643 scopus 로고
    • A coupled KdV equation is one case of the four-reduction of the KP hierarchy
    • J. Satsuma and R. Hirota, A coupled KdV equation is one case of the four-reduction of the KP hierarchy, J. Phys. Soc. Japan 51 (1982) 3390-3397.
    • (1982) J. Phys. Soc. Japan , vol.51 , pp. 3390-3397
    • Satsuma, J.1    Hirota, R.2
  • 43
    • 0001395372 scopus 로고
    • A method for finding N-soliton solutions of the K.d.V. equation and K.d.V.-like equation
    • K. Sawada and T. Kotera, A method for finding N-soliton solutions of the K.d.V. equation and K.d.V.-like equation, Prog. Theor. Phys. 51 (1974) 1355-1367.
    • (1974) Prog. Theor. Phys. , vol.51 , pp. 1355-1367
    • Sawada, K.1    Kotera, T.2
  • 44
    • 0002681157 scopus 로고
    • Separation of variables - New trends
    • E. K. Sklyanin, Separation of variables - New trends -, Prog. Theor. Phys. Suppl. 118 (1995) 35-60.
    • (1995) Prog. Theor. Phys. Suppl. , vol.118 , pp. 35-60
    • Sklyanin, E.K.1
  • 45
    • 4243799764 scopus 로고
    • Sur une classe de problèmes de dynamique
    • P. Stäckel, Sur une classe de problèmes de Dynamique, C. R. Acad. Sc. Paris 116 (1893) 485-487.
    • (1893) C. R. Acad. Sc. Paris , vol.116 , pp. 485-487
    • Stäckel, P.1
  • 46
    • 0001296893 scopus 로고
    • Sur une classe de problèmes de Dynamique, qui se réduisent à des quadratures
    • Sur une classe de problèmes de Dynamique, qui se réduisent à des quadratures, C. R. Acad. Sc. Paris 116 (1893) 1284-1286.
    • (1893) C. R. Acad. Sc. Paris , vol.116 , pp. 1284-1286
  • 48
    • 0035981840 scopus 로고    scopus 로고
    • Integration of a generalized Hénon-Heiles Hamiltonian
    • nlin.SI/0112030
    • C. Verhoeven, M. Musette and R. Conte, Integration of a generalized Hénon-Heiles Hamiltonian, J. Math. Phys. 43 (2002) 1906-1915. nlin.SI/0112030.
    • (2002) J. Math. Phys. , vol.43 , pp. 1906-1915
    • Verhoeven, C.1    Musette, M.2    Conte, R.3
  • 49
    • 30444445724 scopus 로고    scopus 로고
    • On reductions of some KdV-type systems and their link to the quartic Hénon-Heiles Hamiltonian
    • ed. P. van Moerbeke (Kluwer, Dordrecht). nlin.SI/0405034
    • C. Verhoeven, M. Musette and R. Conte, On reductions of some KdV-type systems and their link to the quartic Hénon-Heiles Hamiltonian, 12 pages, Bilinear integrable systems - from classical to quantum, continuous to discrete, ed. P. van Moerbeke (Kluwer, Dordrecht, 2004). nlin.SI/0405034.
    • (2004) Bilinear Integrable Systems - From Classical to Quantum, Continuous to Discrete , pp. 12
    • Verhoeven, C.1    Musette, M.2    Conte, R.3
  • 50
    • 0000838624 scopus 로고
    • Separability of an integrable case of the Hénon-Heiles system
    • S. Wojciechowski, Separability of an integrable case of the Hénon-Heiles system, Phys. Lett. A 100 (1984) 277-278.
    • (1984) Phys. Lett. A , vol.100 , pp. 277-278
    • Wojciechowski, S.1
  • 51
    • 0022080497 scopus 로고
    • Integrability of one particle in a perturbed central quartic potential
    • S. Wojciechowski, Integrability of one particle in a perturbed central quartic potential, Physica Scripta 31 (1985) 433-438.
    • (1985) Physica Scripta , vol.31 , pp. 433-438
    • Wojciechowski, S.1


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