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Volumn 1, Issue 1, 2000, Pages 173-191

Solution of certain integrable dynamical systems of Ruijsenaars-Schneider type with completely periodic trajectories

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EID: 0039608333     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001000     Document Type: Article
Times cited : (14)

References (30)
  • 1
    • 0031518164 scopus 로고    scopus 로고
    • A class of integrable Hamiltonian systems whose solutions are (perhaps) all completely periodic
    • Calogero, F.: A class of integrable Hamiltonian systems whose solutions are (perhaps) all completely periodic. J.Math. Phys. 38, 5711-5719 (1997).
    • (1997) J.Math. Phys. , vol.38 , pp. 5711-5719
    • Calogero, F.1
  • 2
    • 33947149281 scopus 로고    scopus 로고
    • Tricks of the trade: Relating and deriving solvable and integrable dynamical systems
    • To appear, held at the Centre de Recherches Mathématiques de l'Université de Montréal, Canada, in March (Springer, in press)
    • Calogero, F.: Tricks of the trade: relating and deriving solvable and integrable dynamical systems. To appear in the Proceedings of the International Workshop on Calogero-Moser-Sutherland type models, held at the Centre de Recherches Mathématiques de l'Université de Montréal, Canada, in March 1997 (Springer, in press).
    • (1997) Proceedings of the International Workshop on Calogero-Moser-Sutherland Type Models
    • Calogero, F.1
  • 3
    • 51249187156 scopus 로고
    • Motion of poles and zeros of nonlinear and linear partial differential equations and related many-body problems
    • Calogero, F.: Motion of poles and zeros of nonlinear and linear partial differential equations and related many-body problems. Nuovo Cimento 43B, 177-241 (1978).
    • (1978) Nuovo Cimento , vol.43 B , pp. 177-241
    • Calogero, F.1
  • 4
    • 0001574684 scopus 로고
    • The Lax representation for an integrable class of relativistic dynamical systems
    • Bruschi, M., Calogero, F.: The Lax representation for an integrable class of relativistic dynamical systems. Commun Math. Phys. 109, 481-492 (1987).
    • (1987) Commun Math. Phys. , vol.109 , pp. 481-492
    • Bruschi, M.1    Calogero, F.2
  • 5
    • 0030532332 scopus 로고    scopus 로고
    • A solvable N-body problem in the plane. I
    • Calogero, F.: A solvable N-body problem in the plane. I. J. Math. Phys. 37, 1735-1759 (1996).
    • (1996) J. Math. Phys. , vol.37 , pp. 1735-1759
    • Calogero, F.1
  • 6
    • 0032342789 scopus 로고    scopus 로고
    • Integrable and solvable many-body problems in the plane via complexification
    • Calogero, F.: Integrable and solvable many-body problems in the plane via complexification. J. Math. Phys., 39, 5268-5291 (1998).
    • (1998) J. Math. Phys. , vol.39 , pp. 5268-5291
    • Calogero, F.1
  • 7
    • 0011546968 scopus 로고
    • Classical integrable finite-dimensional systems related to Lie algebras
    • Olshanetsky, M.A., Perelomov, A.M.: Classical integrable finite-dimensional systems related to Lie algebras. Phys. Rep. 71, 313-400 (1981).
    • (1981) Phys. Rep. , vol.71 , pp. 313-400
    • Olshanetsky, M.A.1    Perelomov, A.M.2
  • 8
    • 14944363471 scopus 로고    scopus 로고
    • A new class of integrable systems and its relation to solitons
    • See, for instance: Ruijsenaars, S.N.M., Schneider, H.: A new class of integrable systems and its relation to solitons. Ann. Phys. (NY) 170, 370-405 (1986); Ruijsenaars, S.N.M.: Systems of Calogero-Moser type. Proceedings of the 1994 Banff Summer School on Particles and Fields, CRM Proceedings and Lecture Notes (in press), and the papers referred to there; van Diejen, J.F.: Families of commuting difference operators. PhD Thesis, University of Amsterdam, 28 June 1994.
    • (1986) Ann. Phys. (NY) , vol.170 , pp. 370-405
    • Ruijsenaars, S.N.M.1    Schneider, H.2
  • 9
    • 14944363471 scopus 로고    scopus 로고
    • Systems of Calogero-Moser type
    • (in press), and the papers referred to there
    • See, for instance: Ruijsenaars, S.N.M., Schneider, H.: A new class of integrable systems and its relation to solitons. Ann. Phys. (NY) 170, 370-405 (1986); Ruijsenaars, S.N.M.: Systems of Calogero-Moser type. Proceedings of the 1994 Banff Summer School on Particles and Fields, CRM Proceedings and Lecture Notes (in press), and the papers referred to there; van Diejen, J.F.: Families of commuting difference operators. PhD Thesis, University of Amsterdam, 28 June 1994.
    • Proceedings of the 1994 Banff Summer School on Particles and Fields, CRM Proceedings and Lecture Notes
    • Ruijsenaars, S.N.M.1
  • 10
    • 14944363471 scopus 로고    scopus 로고
    • PhD Thesis, University of Amsterdam, 28 June
    • See, for instance: Ruijsenaars, S.N.M., Schneider, H.: A new class of integrable systems and its relation to solitons. Ann. Phys. (NY) 170, 370-405 (1986); Ruijsenaars, S.N.M.: Systems of Calogero-Moser type. Proceedings of the 1994 Banff Summer School on Particles and Fields, CRM Proceedings and Lecture Notes (in press), and the papers referred to there; van Diejen, J.F.: Families of commuting difference operators. PhD Thesis, University of Amsterdam, 28 June 1994.
    • (1994) Families of Commuting Difference Operators
    • Van Diejen, J.F.1
  • 11
    • 0345860250 scopus 로고
    • Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles
    • Krichever, I.M.: Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles. Funct. Anal. Appl. 14, 282-289 (1981).
    • (1981) Funct. Anal. Appl. , vol.14 , pp. 282-289
    • Krichever, I.M.1
  • 12
    • 84956259690 scopus 로고
    • Spin generalizations of the RS model, nonabelian 2D Toda chain and representations of Sklyanin algebra
    • Krichever, I.M., Zabrodin, A.V.: Spin generalizations of the RS model, nonabelian 2D Toda chain and representations of Sklyanin algebra. Russ. Math. Surv. 50, 1101-1150 (1995).
    • (1995) Russ. Math. Surv. , vol.50 , pp. 1101-1150
    • Krichever, I.M.1    Zabrodin, A.V.2
  • 13
    • 13644277471 scopus 로고
    • Hamiltonian systems of Calogero-type, and two-dimensional Yang-Mills theory
    • Gorsky, A., Nekrasov, N.: Hamiltonian systems of Calogero-type, and two-dimensional Yang-Mills theory. Nuclear Phys. B414, 213-238 (1994); Relativistic Calogero-Moser model as gauged WZW theory. Nuclear Phys. B436, 582-608 (1995).
    • (1994) Nuclear Phys. , vol.B414 , pp. 213-238
    • Gorsky, A.1    Nekrasov, N.2
  • 14
    • 0039493494 scopus 로고
    • Relativistic Calogero-Moser model as gauged WZW theory
    • Gorsky, A., Nekrasov, N.: Hamiltonian systems of Calogero-type, and two-dimensional Yang-Mills theory. Nuclear Phys. B414, 213-238 (1994); Relativistic Calogero-Moser model as gauged WZW theory. Nuclear Phys. B436, 582-608 (1995).
    • (1995) Nuclear Phys. , vol.B436 , pp. 582-608
  • 17
    • 84980148563 scopus 로고
    • Hamiltonian group actions and dynamical systems of Calogero type
    • Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian group actions and dynamical systems of Calogero type. Commun. Pure Appl. Math. 31, 481-507 (1978).
    • (1978) Commun. Pure Appl. Math. , vol.31 , pp. 481-507
    • Kazhdan, D.1    Kostant, B.2    Sternberg, S.3
  • 18
    • 0001849572 scopus 로고
    • Canonical partition functions of Hamiltonian systems and the stationary phase formula
    • Françoise, J.-P.: Canonical partition functions of Hamiltonian systems and the stationary phase formula. Commun. Math. Phys. 117, 37-47 (1988).
    • (1988) Commun. Math. Phys. , vol.117 , pp. 37-47
    • Françoise, J.-P.1
  • 19
    • 0008025629 scopus 로고
    • Matrix differential equations and Hamiltonian systems of quartic type
    • Françoise, J.-P., Ragnisco, O.: Matrix differential equations and Hamiltonian systems of quartic type. Ann. Inst. H. Poincaré 49, 369-375 (1989).
    • (1989) Ann. Inst. H. Poincaré , vol.49 , pp. 369-375
    • Françoise, J.-P.1    Ragnisco, O.2
  • 20
    • 0040050919 scopus 로고    scopus 로고
    • The Ruijsenaars-Schneider model
    • Braden, H.W., Sasaki, R.: The Ruijsenaars-Schneider model. Prog. Theor. Phys. 97, 1001-1015 (1997).
    • (1997) Prog. Theor. Phys. , vol.97 , pp. 1001-1015
    • Braden, H.W.1    Sasaki, R.2
  • 21
    • 84874962985 scopus 로고
    • Convexity and commuting Hamiltonians
    • Atiyah, M.: Convexity and commuting Hamiltonians. Bull. London Math. Soc. 14, 1-15 (1982); Colin de Verdière, Y.: Spectre joint d'opérateurs pseudodifférentiels qui commutent. II - Le cas intégrable. Math. Zeit. 171, 169-182 (1980); Guillemin, V., Sternberg, S.: Symplectic Techniques in Physics. Cambridge University Press, Cambridge (1984).
    • (1982) Bull. London Math. Soc. , vol.14 , pp. 1-15
    • Atiyah, M.1
  • 22
    • 84874962985 scopus 로고
    • Spectre joint d'opérateurs pseudodifférentiels qui commutent. II - Le cas intégrable
    • Atiyah, M.: Convexity and commuting Hamiltonians. Bull. London Math. Soc. 14, 1-15 (1982); Colin de Verdière, Y.: Spectre joint d'opérateurs pseudodifférentiels qui commutent. II - Le cas intégrable. Math. Zeit. 171, 169-182 (1980); Guillemin, V., Sternberg, S.: Symplectic Techniques in Physics. Cambridge University Press, Cambridge (1984).
    • (1980) Math. Zeit. , vol.171 , pp. 169-182
    • Colin De Verdière, Y.1
  • 23
    • 84874962985 scopus 로고
    • Cambridge University Press, Cambridge
    • Atiyah, M.: Convexity and commuting Hamiltonians. Bull. London Math. Soc. 14, 1-15 (1982); Colin de Verdière, Y.: Spectre joint d'opérateurs pseudodifférentiels qui commutent. II - Le cas intégrable. Math. Zeit. 171, 169-182 (1980); Guillemin, V., Sternberg, S.: Symplectic Techniques in Physics. Cambridge University Press, Cambridge (1984).
    • (1984) Symplectic Techniques in Physics
    • Guillemin, V.1    Sternberg, S.2
  • 24
    • 85013288774 scopus 로고    scopus 로고
    • Quantum dynamical R-matrices and quantum Frobenius group
    • press
    • Arutyunov, G.E., Frolov, S.A.: Quantum dynamical R-matrices and quantum Frobenius group. Commun. Math. Phys. (in press); On Hamiltonian structure of the spin RS model. J. Phys. A: Math. Gen. (submitted to).
    • Commun. Math. Phys.
    • Arutyunov, G.E.1    Frolov, S.A.2
  • 25
    • 85013237393 scopus 로고    scopus 로고
    • On Hamiltonian structure of the spin RS model
    • submitted to
    • Arutyunov, G.E., Frolov, S.A.: Quantum dynamical R-matrices and quantum Frobenius group. Commun. Math. Phys. (in press); On Hamiltonian structure of the spin RS model. J. Phys. A: Math. Gen. (submitted to).
    • J. Phys. A: Math. Gen.
  • 27
    • 0010118968 scopus 로고    scopus 로고
    • The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
    • Avan, J., Babelon, O., Billey, E.: The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems. Commun. Math. Phys. 178, 281-299 (1996).
    • (1996) Commun. Math. Phys. , vol.178 , pp. 281-299
    • Avan, J.1    Babelon, O.2    Billey, E.3
  • 28
    • 0000884682 scopus 로고
    • Conformal field theory and integrable systems associated with elliptic curves
    • Zürich
    • Felder, G.: Conformal field theory and integrable systems associated with elliptic curves. Proceedings of the International Congress of Mathematicians, 1247-1255, Zürich (1994).
    • (1994) Proceedings of the International Congress of Mathematicians , pp. 1247-1255
    • Felder, G.1
  • 30
    • 0039054087 scopus 로고    scopus 로고
    • Why is the Ruijsenaars-Schneider hierarchy governed by the same R-matrix as the Calogero-Moser one?
    • Suris, Yu.B.: Why is the Ruijsenaars-Schneider hierarchy governed by the same R-matrix as the Calogero-Moser one? Phys. Rev. A225, 253-261 (1997).
    • (1997) Phys. Rev. , vol.A225 , pp. 253-261
    • Suris, Y.B.1


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