메뉴 건너뛰기




Volumn 31, Issue 4, 1999, Pages 265-286

Completely integrable systems: Jacobi's heritage

Author keywords

Completely integrable systems

Indexed keywords


EID: 0033212334     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(99)00015-7     Document Type: Article
Times cited : (12)

References (52)
  • 1
    • 34250286595 scopus 로고
    • On a trace functional for pseudo-differential operators and the symplectic structure of the Korteweg-de Vries equation
    • M. Adler, On a trace functional for pseudo-differential operators and the symplectic structure of the Korteweg-de Vries equation, Invent. Math. 50 (1979) 219-248.
    • (1979) Invent. Math. , vol.50 , pp. 219-248
    • Adler, M.1
  • 2
    • 49149147606 scopus 로고
    • Completely integrable systems, euclidean lie algebras and curves
    • M. Adler, P. van Moerbeke, Completely integrable systems, euclidean lie algebras and curves, Adv. Math. 38 (1980) 267-317.
    • (1980) Adv. Math. , vol.38 , pp. 267-317
    • Adler, M.1    Van Moerbeke, P.2
  • 3
    • 49149144090 scopus 로고
    • Linearization of hamiltonian systems, Jacobi varieties and representation theory
    • M. Adler, P. van Moerbeke, Linearization of hamiltonian systems, Jacobi varieties and representation theory, Adv. Math. 38 (1980) 318-379.
    • (1980) Adv. Math. , vol.38 , pp. 318-379
    • Adler, M.1    Van Moerbeke, P.2
  • 4
    • 0002995659 scopus 로고
    • Kowalewski's asymptotic method, Kac-Moody lie algebras and regularization
    • M. Adler, P. van Moerbeke, Kowalewski's asymptotic method, Kac-Moody lie algebras and regularization, Comm. Math. Phys. 83 (1982) 83-106.
    • (1982) Comm. Math. Phys. , vol.83 , pp. 83-106
    • Adler, M.1    Van Moerbeke, P.2
  • 5
    • 0001183233 scopus 로고
    • The algebraic complete integrability of geodesic flow on SO (4)
    • M. Adler, P. van Moerbeke, The algebraic complete integrability of geodesic flow on SO (4), Invent. Math. 67 (1982) 297-331.
    • (1982) Invent. Math. , vol.67 , pp. 297-331
    • Adler, M.1    Van Moerbeke, P.2
  • 6
    • 0000367988 scopus 로고
    • The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO (4)- A two-dimensional family of Lax pairs
    • M. Adler, P. van Moerbeke, The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO (4)- A two-dimensional family of Lax pairs, Comm. Math. Phys. 113 (1988) 659-700.
    • (1988) Comm. Math. Phys. , vol.113 , pp. 659-700
    • Adler, M.1    Van Moerbeke, P.2
  • 8
    • 0001674867 scopus 로고
    • Der bewegung eines starren körpers in einen flüssigkeit
    • A. Clebsch, Der bewegung eines starren körpers in einen flüssigkeit, Math. Ann. 3 (1971) 238-268.
    • (1971) Math. Ann. , vol.3 , pp. 238-268
    • Clebsch, A.1
  • 9
    • 0002113216 scopus 로고
    • Periodic and conditionally periodic analogues of multi-soliton solutions of the KdV equation
    • B.A. Dubrovin, S.P. Novikov, Periodic and conditionally periodic analogues of multi-soliton solutions of the KdV equation, Dokl. Akad. Nauk URSS 6 (1974) 2131-2144.
    • (1974) Dokl. Akad. Nauk URSS , vol.6 , pp. 2131-2144
    • Dubrovin, B.A.1    Novikov, S.P.2
  • 10
    • 25344451956 scopus 로고
    • The Toda lattice I
    • H. Flaschka, The Toda lattice I, Phys. Rev. B 9 (1974) 1924-1925.
    • (1974) Phys. Rev. B , vol.9 , pp. 1924-1925
    • Flaschka, H.1
  • 11
  • 13
    • 0000889453 scopus 로고
    • Linearizing flows and a comological interpretation of Lax equations
    • P.A. Griffiths, Linearizing flows and a comological interpretation of Lax equations, Amer. J. Math. 107 (1985) 1445-1483.
    • (1985) Amer. J. Math. , vol.107 , pp. 1445-1483
    • Griffiths, P.A.1
  • 14
    • 0001133547 scopus 로고
    • Geodesic flow on SO (4) and abelian surfaces
    • L. Haine, Geodesic flow on SO (4) and abelian surfaces, Math. Ann. 263 (1983) 435-472.
    • (1983) Math. Ann. , vol.263 , pp. 435-472
    • Haine, L.1
  • 15
    • 33744740330 scopus 로고
    • On the construction of monopoles
    • N.J. Hitchin, On the construction of monopoles, Comm. Math. Phys. 89 (1983) 145-190.
    • (1983) Comm. Math. Phys. , vol.89 , pp. 145-190
    • Hitchin, N.J.1
  • 16
    • 0003431502 scopus 로고
    • Vorlesungen über dynamik
    • Supplementband, Berlin
    • C.G.J. Jacobi, Vorlesungen über dynamik, in: Gesammelte Werke, Supplementband, Berlin, 1980.
    • (1980) Gesammelte Werke
    • Jacobi, C.G.J.1
  • 17
    • 0000167758 scopus 로고
    • Geodesics on the ellipsoid
    • H. Knörrer, Geodesics on the ellipsoid, Invent. Math. 59 (1980) 119-144.
    • (1980) Invent. Math. , vol.59 , pp. 119-144
    • Knörrer, H.1
  • 18
    • 0000876641 scopus 로고
    • The solution to a generalized Toda lattice and representation theory
    • B. Kostant, The solution to a generalized Toda lattice and representation theory, Adv. Math. 34 (1979) 195-338.
    • (1979) Adv. Math. , vol.34 , pp. 195-338
    • Kostant, B.1
  • 19
    • 0009309816 scopus 로고
    • Uber die bewegung eines festen körpers in einer flüssigkeit I, II
    • 89-110
    • F. Kötter, Uber die bewegung eines festen körpers in einer flüssigkeit I, II, J. Riene Angew. Math. 109 (1892) 51-81, 89-110.
    • (1892) J. Riene Angew. Math. , vol.109 , pp. 51-81
    • Kötter, F.1
  • 20
    • 0009410583 scopus 로고
    • Die von steklow und lyapunov entdeckten integralen fälle der bewegung eines körpers in einen flüssigkeit sitzungsber
    • Berlin
    • F. Kötter, Die von steklow und lyapunov entdeckten integralen fälle der bewegung eines körpers in einen flüssigkeit sitzungsber, Königlich Preussische Akad. D. Wiss., Berlin, vol. 6, 1900, pp. 79-87.
    • (1900) Königlich Preussische Akad. D. Wiss. , vol.6 , pp. 79-87
    • Kötter, F.1
  • 21
    • 34250579023 scopus 로고
    • Sur le problème de la rotation d'un corps solide autour d'un point fixe
    • S. Kowalewski, Sur le problème de la rotation d'un corps solide autour d'un point fixe, Acta Math. 12 (1889) 177-232.
    • (1889) Acta Math. , vol.12 , pp. 177-232
    • Kowalewski, S.1
  • 22
    • 0001970782 scopus 로고
    • Integrability and non-integrability in hamiltonian mechanics
    • Transl 1, Russian Math. Surveys 38 (1983) 1-76
    • V.V. Kozlov, Integrability and non-integrability in hamiltonian mechanics, Uspekhi Mat. Nauk 38 (1983) 3-67 (Transl 1, Russian Math. Surveys 38 (1983) 1-76).
    • (1983) Uspekhi Mat. Nauk , vol.38 , pp. 3-67
    • Kozlov, V.V.1
  • 23
    • 0009419966 scopus 로고
    • Algebro-geometrical construction of the Zakharov Shabat equations and their periodic solutions
    • M. Krichever, Algebro-geometrical construction of the Zakharov Shabat equations and their periodic solutions, Sov. Math. Dokl. 17 (1976) 394-397.
    • (1976) Sov. Math. Dokl. , vol.17 , pp. 394-397
    • Krichever, M.1
  • 24
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • P. 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.1
  • 25
    • 0009367975 scopus 로고
    • The Gelfand-Dikii hamiltonian operator and the coadjoint representation of the Volterra group
    • D.R. Lebedev, Yu. I. Manin, The Gelfand-Dikii hamiltonian operator and the coadjoint representation of the Volterra group, Func. Anal. Appl. 13 (1979) 40-46.
    • (1979) Func. Anal. Appl. , vol.13 , pp. 40-46
    • Lebedev, D.R.1    Manin, Y.I.2
  • 26
    • 84878879948 scopus 로고
    • Equation de Korteweg-de Vries
    • U.C.L., Louvainla-Neuve, Belgique
    • A. Lesfari, Equation de Korteweg-de Vries, Mem. Dpt. Maths. Fac. Sc., U.C.L., Louvainla-Neuve, Belgique, 1982, pp. 1-113.
    • (1982) Mem. Dpt. Maths. Fac. Sc. , pp. 1-113
    • Lesfari, A.1
  • 27
    • 0009311185 scopus 로고
    • Une approche systématique à la résolution due corps solide de kowalewski
    • Série I
    • A. Lesfari, Une approche systématique à la résolution due corps solide de kowalewski, C. R. Acad. Sc. Paris, t. 302, Série I, 1986, pp. 347-350.
    • (1986) C. R. Acad. Sc. Paris , vol.302 , pp. 347-350
    • Lesfari, A.1
  • 28
    • 0009375260 scopus 로고
    • Une approche systématique à la résolution des systémes intégrables
    • 15-19 juin E.H.T.P., Casablanca, Maroc (Conférences organisées en l'honneur du Pr. A. Lichnerowicz)
    • E École de GéMétrie- Analyse (15-19 juin 1987), p. 83, E.H.T.P., Casablanca, Maroc (Conférences organisées en l'honneur du Pr. A. Lichnerowicz).
    • (1987) E École de GéMétrie- Analyse , pp. 83
    • Lesfari, A.1
  • 31
    • 0009310364 scopus 로고
    • Sochepress-Université, Casablanca, Maroc
    • A. Lesfari, Eléments D'analyse, Sochepress-Université, Casablanca, Maroc, 1991.
    • (1991) Eléments D'analyse
    • Lesfari, A.1
  • 32
    • 0009412391 scopus 로고    scopus 로고
    • On affine surface that can be completed by a smooth curve
    • A. Lesfari, On affine surface that can be completed by a smooth curve, Results Math. 35 (1999) 107-118.
    • (1999) Results Math. , vol.35 , pp. 107-118
    • Lesfari, A.1
  • 33
    • 0009309253 scopus 로고    scopus 로고
    • Geodesic flow on SO(4), Kac-Moody lie algebra and its singularities in the complex t-plane
    • in press
    • A. Lesfari, Geodesic flow on SO(4), Kac-Moody lie algebra and its singularities in the complex t-plane, Publicacions Matemàtiques 43 (1999), in press.
    • (1999) Publicacions Matemàtiques , vol.43
    • Lesfari, A.1
  • 34
    • 0009358822 scopus 로고    scopus 로고
    • Une méthode de compactification de variétés liées aux systèmes dynamiques, cahiers de la recherche
    • A. Lesfari, Une méthode de compactification de variétés liées aux systèmes dynamiques, cahiers de la recherche, Rectorat-université Hassan II Aïn Chock 1(1) (1999) 147-157.
    • (1999) Rectorat-université Hassan II Aïn Chock , vol.1 , Issue.1 , pp. 147-157
    • Lesfari, A.1
  • 36
  • 37
    • 0001789746 scopus 로고
    • Remarks on the integrals of the Euler equations of the n-dimensional heavy top
    • S.V. Manakov, Remarks on the integrals of the Euler equations of the n-dimensional heavy top, Func. Anal. Appl. 10 (1976) 93-94.
    • (1976) Func. Anal. Appl. , vol.10 , pp. 93-94
    • Manakov, S.V.1
  • 38
    • 0001834849 scopus 로고
    • On the stability of the center for time-periodic perturbations
    • V.K. Melnikov, On the stability of the center for time-periodic perturbations, Trans. Mosc. Math. Soc. 12 (1963) 1-57.
    • (1963) Trans. Mosc. Math. Soc. , vol.12 , pp. 1-57
    • Melnikov, V.K.1
  • 39
    • 0002449448 scopus 로고
    • The spectrum of Jacobi matrices
    • P. van Moerbeke, The spectrum of Jacobi matrices, Invent, Math. 37 (1976) 45-81.
    • (1976) Invent, Math. , vol.37 , pp. 45-81
    • Van Moerbeke, P.1
  • 40
    • 79958233764 scopus 로고
    • Algebraic complete integrability of hamiltonian systems and Kac-Moody lie algebras
    • Warszawa
    • P. van Moerbeke, Algebraic complete integrability of hamiltonian systems and Kac-Moody lie algebras, Proc. Int. Cong. Math., Warszawa, 1983.
    • (1983) Proc. Int. Cong. Math.
    • Van Moerbeke, P.1
  • 41
    • 0001827098 scopus 로고
    • The spectrum of difference operators and algebraic curves
    • P. van Moerbeke, D. Mumford, The spectrum of difference operators and algebraic curves, Acta Math. 143 (1979) 93-154.
    • (1979) Acta Math. , vol.143 , pp. 93-154
    • Van Moerbeke, P.1    Mumford, D.2
  • 42
    • 34347230069 scopus 로고
    • Three integrable hamiltonian systems connected with isospectral deformations
    • J. Moser, Three integrable hamiltonian systems connected with isospectral deformations, Adv. Math. 16 (1975) 197-219.
    • (1975) Adv. Math. , vol.16 , pp. 197-219
    • Moser, J.1
  • 43
    • 0009372299 scopus 로고
    • Lecture delivered at the symposium in honor of S.S. Chern, Berkeley, Springer, Berlin
    • J. Moser, Geometry of Quadrics and Spectral Theory, Lecture delivered at the symposium in honor of S.S. Chern, Berkeley, 1979, Springer, Berlin, 1980.
    • (1979) Geometry of Quadrics and Spectral Theory
    • Moser, J.1
  • 44
    • 0003358349 scopus 로고
    • Tata lectures on theta. II
    • Birkhaüser, Boston
    • D. Mumford, Tata lectures on theta. II. Progress in Math., Birkhaüser, Boston, 1982.
    • (1982) Progress in Math.
    • Mumford, D.1
  • 45
    • 84919913673 scopus 로고
    • De problemate quodam mechanics, quod ad primam integralium ultraellipticorum classem revocatur
    • C. Neumann, De problemate quodam mechanics, quod ad primam integralium ultraellipticorum classem revocatur, Reine und Angew. Math. J. 56 (1859) 44-63.
    • (1859) Reine und Angew. Math. J. , vol.56 , pp. 44-63
    • Neumann, C.1
  • 46
    • 0009410584 scopus 로고
    • On the motion of a solid in a liquid
    • V. Steklov, On the motion of a solid in a liquid, Math. Ann. 42 (1893) 273-394.
    • (1893) Math. Ann. , vol.42 , pp. 273-394
    • Steklov, V.1
  • 47
    • 34250248977 scopus 로고
    • Systems of Toda type, inverse spectral problems and representation theory
    • W. Symes, Systems of Toda type, inverse spectral problems and representation theory, Invent. Math. 59 (1980) 13-53.
    • (1980) Invent. Math. , vol.59 , pp. 13-53
    • Symes, W.1
  • 48
    • 34250146236 scopus 로고
    • Necessary conditions for the existence of algebraic first integrals. I. Kowalewski 's exponents. II. Conditions for algebraic integrability
    • 381-399
    • H. Yoshida, Necessary conditions for the existence of algebraic first integrals. I. Kowalewski 's exponents. II. Conditions for algebraic integrability. Celestial Mech. 31 (1983) 363-379, 381-399.
    • (1983) Celestial Mech. , vol.31 , pp. 363-379
    • Yoshida, H.1
  • 49
    • 0009372301 scopus 로고
    • A schema for integrating the non-linear equations of math. Physics by the method of the inverse scattering problem I
    • V. Zaharov, A. Shabat, A schema for integrating the non-linear equations of math. Physics by the method of the inverse scattering problem I. Funct. Anal. Appl. 8 (1974).
    • (1974) Funct. Anal. Appl. , vol.8
    • Zaharov, V.1    Shabat, A.2
  • 50
    • 0000511722 scopus 로고
    • Splitting of sepatrices, branching of solutions and non-existence of an integral in the dynamics of a solid body
    • Transl. 1 (1982) 283-298
    • S.L. Ziglin, Splitting of sepatrices, branching of solutions and non-existence of an integral in the dynamics of a solid body. Trans. Moscow Math. Soc. 41 (1980) 287-303 (Transl. 1 (1982) 283-298).
    • (1980) Trans. Moscow Math. Soc. , vol.41 , pp. 287-303
    • Ziglin, S.L.1
  • 51
    • 0041020915 scopus 로고
    • Branching of solutions and non-existence of first integrals in hamiltonian mechanics. 1
    • S.L. Ziglin, Branching of solutions and non-existence of first integrals in hamiltonian mechanics. 1. Funct. Anal. Appl. 16 (1982) 30-41.
    • (1982) Funct. Anal. Appl. , vol.16 , pp. 30-41
    • Ziglin, S.L.1
  • 52
    • 14344258193 scopus 로고
    • Branching of solutions and non-existence of first integrals in hamiltonian mechanics. 2
    • S.L. Ziglin, Branching of solutions and non-existence of first integrals in hamiltonian mechanics. 2. Funct. Anal. Appl. 17 (1983) 8-23.
    • (1983) Funct. Anal. Appl. , vol.17 , pp. 8-23
    • Ziglin, S.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.