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Volumn 180, Issue 3, 1996, Pages 529-586

Theory of tensor invariants of integrable Hamiltonian systems. I. Incompatible poisson structures

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EID: 0003313265     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02099623     Document Type: Article
Times cited : (39)

References (55)
  • 2
    • 0002764805 scopus 로고
    • Proof of A.N. Kolmogorov's theorem on the preservation of quasi-periodic motions under small perturbation of the Hamiltonian
    • Ser. 5
    • Arnold, V.I.: Proof of A.N. Kolmogorov's theorem on the preservation of quasi-periodic motions under small perturbation of the Hamiltonian. Uspekhi Mat. Nauk. U.S.S.R. 18, Ser. 5, 13-40 (1963)
    • (1963) Uspekhi Mat. Nauk. U.S.S.R. , vol.18 , pp. 13-40
    • Arnold, V.I.1
  • 4
    • 0004223966 scopus 로고
    • Providence, Rhode Island: American Mathematical Society
    • Birkhoff, G.D.: Dynamical systems. Providence, Rhode Island: American Mathematical Society, 1966
    • (1966) Dynamical Systems
    • Birkhoff, G.D.1
  • 5
    • 0009414484 scopus 로고
    • Invariant incompatible poisson structures
    • Bogoyavlenskij, O.I.: Invariant incompatible Poisson structures. Proc. R. Soc. Lond. A 450, 723-730 (1995)
    • (1995) Proc. R. Soc. Lond. A , vol.450 , pp. 723-730
    • Bogoyavlenskij, O.I.1
  • 6
    • 0039689509 scopus 로고
    • Incompatible poisson structures and integrable hamiltonian systems
    • Bogoyavlenskij, O.I.: Incompatible Poisson structures and integrable Hamiltonian systems. C. R. Math. Rep. Acad. Sci. Canada 17, 123-128 (1995)
    • (1995) C. R. Math. Rep. Acad. Sci. Canada , vol.17 , pp. 123-128
    • Bogoyavlenskij, O.I.1
  • 8
    • 0039097366 scopus 로고
    • Systemes bihamiltoniens et complète intégrabilité en dimension 4
    • S. I
    • Brouzet, R.: Systemes bihamiltoniens et complète intégrabilité en dimension 4. C. R. Acad. Sci. Paris 311, S. I, 895-898 (1990)
    • (1990) C. R. Acad. Sci. Paris , vol.311 , pp. 895-898
    • Brouzet, R.1
  • 9
    • 21144470493 scopus 로고
    • About the existence of recursion operators for completely integrable Hamiltonian systems near a Liouville torus
    • Brouzet, R.: About the existence of recursion operators for completely integrable Hamiltonian systems near a Liouville torus. J. Math. Phys. 34, 1309-1313 (1993)
    • (1993) J. Math. Phys. , vol.34 , pp. 1309-1313
    • Brouzet, R.1
  • 10
    • 38249005865 scopus 로고
    • Gèomètrie des systèmes bihamiltoniens
    • N.S.
    • Brouzet, R., Molino, P., Turiel, F.J.: Gèomètrie des systèmes bihamiltoniens. Indag. Mathem., N.S., 4, 269-296 (1993)
    • (1993) Indag. Mathem. , vol.4 , pp. 269-296
    • Brouzet, R.1    Molino, P.2    Turiel, F.J.3
  • 11
    • 0002610687 scopus 로고
    • Conditions for the complete integrability of a dynamical system admitting alternative Lagrangians
    • Crampin, M., Marmo, G., Rubano, C.: Conditions for the complete integrability of a dynamical system admitting alternative Lagrangians. Phys. Lett. A 97, 88-90 (1983)
    • (1983) Phys. Lett. A , vol.97 , pp. 88-90
    • Crampin, M.1    Marmo, G.2    Rubano, C.3
  • 12
    • 0000586113 scopus 로고
    • A systematic study of the Toda lattice
    • Das, A., Okubo, S.: A systematic study of the Toda lattice. Ann. Phys. 190, 215-232 (1989)
    • (1989) Ann. Phys. , vol.190 , pp. 215-232
    • Das, A.1    Okubo, S.2
  • 13
    • 51649166879 scopus 로고
    • A new characterization on completely integrable systems
    • De Fillipo, S., Vilasi, G., Marmo, G., Salerno, M.: A new characterization on completely integrable systems, Nuovo Cimento B 83, 97-112 (1984)
    • (1984) Nuovo Cimento B , vol.83 , pp. 97-112
    • De Fillipo, S.1    Vilasi, G.2    Marmo, G.3    Salerno, M.4
  • 14
    • 0000585131 scopus 로고
    • Sur l'analysis situs des variétés a n dimensions
    • De Rham, G.: Sur l'Analysis situs des variétés a n dimensions. J. de Mathem. Pures and Appl. 10, 115-200 (1931)
    • (1931) J. de Mathem. Pures and Appl. , vol.10 , pp. 115-200
    • De Rham, G.1
  • 16
    • 0000603355 scopus 로고
    • Differential forms in manifolds with boundary
    • Duff, G.F.D.: Differential forms in manifolds with boundary. Ann. Math. 56, 115-127 (1952)
    • (1952) Ann. Math. , vol.56 , pp. 115-127
    • Duff, G.F.D.1
  • 17
    • 0000809059 scopus 로고
    • Harmonic tensors of Riemannian manifolds with boundary
    • Duff, G.F.D., Spencer, D.C.: Harmonic tensors of Riemannian manifolds with boundary. Ann. Math. 56, 128-156 (1952)
    • (1952) Ann. Math. , vol.56 , pp. 128-156
    • Duff, G.F.D.1    Spencer, D.C.2
  • 18
    • 84980167278 scopus 로고
    • On global action-angle coordinates
    • Duistermaat, J.J.: On global action-angle coordinates. Comm. Pure Appl. Math. 33, 687-706 (1980)
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 687-706
    • Duistermaat, J.J.1
  • 19
    • 0001159402 scopus 로고
    • Completely integrable bi-Hamiltonian systems
    • Fernandes, R.L.: Completely integrable bi-Hamiltonian systems. J. Dyn. Diff. Eq. 6, 53-69 (1994)
    • (1994) J. Dyn. Diff. Eq. , vol.6 , pp. 53-69
    • Fernandes, R.L.1
  • 20
    • 0001390841 scopus 로고
    • Applications of hereditary symmetries to nonlinear evolution equations
    • Fuchssteiner, B.: Applications of hereditary symmetries to nonlinear evolution equations. Nonlinear Analysis, Theory, Methods and Applic. 3, 849-862 (1979)
    • (1979) Nonlinear Analysis, Theory, Methods and Applic. , vol.3 , pp. 849-862
    • Fuchssteiner, B.1
  • 21
    • 0001218076 scopus 로고
    • The lie algebra structure of degenerate Hamiltonian and bi-Hamiltonian systems
    • Fuchssteiner, B.: The Lie algebra structure of degenerate Hamiltonian and bi-Hamiltonian systems. Progr. Theor. Phys. 68, 1082-1104 (1982)
    • (1982) Progr. Theor. Phys. , vol.68 , pp. 1082-1104
    • Fuchssteiner, B.1
  • 22
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • Fuchssteiner, B., Fokas, A.S.: Symplectic structures, their Bäcklund transformations and hereditary symmetries. Physica D 4, 47-66 (1981)
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 23
    • 84980193643 scopus 로고
    • Korteweg-de Vries equation and generalizations. VI. Methods for exact solution
    • Gardner, C.S., Greene, J.M., Kruskal, M.D., Miura, R.M.: Korteweg-de Vries Equation and Generalizations. VI. Methods for exact solution. Comm. Pure Appl. Math. 27, 97-133 (1974)
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 97-133
    • Gardner, C.S.1    Greene, J.M.2    Kruskal, M.D.3    Miura, R.M.4
  • 24
    • 25844439585 scopus 로고
    • Hamiltonian operators and algebraic structures related to them
    • Gelfand, I.M., Dorfman, I.Ya.: Hamiltonian operators and algebraic structures related to them. Funct. Anal. Applic. 13, 248-262 (1979)
    • (1979) Funct. Anal. Applic. , vol.13 , pp. 248-262
    • Gelfand, I.M.1    Dorfman, I.Ya.2
  • 25
    • 33745701144 scopus 로고
    • The Schouten bracket and Hamiltonian operators
    • Gelfand, I.M., Dorfman, I.Ya.: The Schouten bracket and Hamiltonian operators. Funct. Anal. Applic. 14, 223-226 (1980)
    • (1980) Funct. Anal. Applic. , vol.14 , pp. 223-226
    • Gelfand, I.M.1    Dorfman, I.Ya.2
  • 26
    • 0001246972 scopus 로고
    • On conservation of conditionally periodic motions under small variations of the Hamiltonian
    • Kolmogorov, A.N.: On conservation of conditionally periodic motions under small variations of the Hamiltonian. Dokl. Akad. Nauk SSSR 98, 527-530 (1954)
    • (1954) Dokl. Akad. Nauk SSSR , vol.98 , pp. 527-530
    • Kolmogorov, A.N.1
  • 27
    • 0001441814 scopus 로고
    • The general theory of dynamical systems and classical mechanics
    • Amsterdam: North-Holland Publ. Co.
    • Kolmogorov, A.N.: The general theory of dynamical systems and classical mechanics. In: Proc. Intern. Congr. Math. 1954, 1. Amsterdam: North-Holland Publ. Co., 1957, pp. 315-333
    • (1957) Proc. Intern. Congr. Math. 1954 , vol.1 , pp. 315-333
    • Kolmogorov, A.N.1
  • 28
    • 0010153808 scopus 로고
    • Géométrie des systèmes bihamiltoniens
    • Press. Univers. de Montreal
    • Kosmann-Schwarzbach, Y.: Géométrie des systèmes bihamiltoniens. Seminaire de Math. Sup., Press. Univers. de Montreal 102, 185-216 (1986)
    • (1986) Seminaire de Math. Sup. , vol.102 , pp. 185-216
    • Kosmann-Schwarzbach, Y.1
  • 30
    • 36449003784 scopus 로고
    • Recursion operators: Meaning and existence for completely integrable systems
    • Landi, G., Marmo, G., Vilasi, G.: Recursion operators: Meaning and existence for completely integrable systems. J. Math. Phys. 35, 808-815 (1994)
    • (1994) J. Math. Phys. , vol.35 , pp. 808-815
    • Landi, G.1    Marmo, G.2    Vilasi, G.3
  • 31
    • 84972540666 scopus 로고
    • Les variétés de poisson et leurs algèbres de lie associées
    • Lichnerowicz, A.: Les variétés de Poisson et leurs algèbres de Lie associées. J. Diff. Geom. 12, 253-300 (1977)
    • (1977) J. Diff. Geom. , vol.12 , pp. 253-300
    • Lichnerowicz, A.1
  • 32
    • 0000970971 scopus 로고
    • Note sur l'intégration des équations différentielles de la dynamique
    • Liouville, J.: Note sur l'intégration des équations différentielles de la Dynamique. J. Math. Pures Appl. 20, 137-138 (1855)
    • (1855) J. Math. Pures Appl. , vol.20 , pp. 137-138
    • Liouville, J.1
  • 33
    • 85079921911 scopus 로고
    • Poisson-nijenhuis structures, truncated loop algebras and Sato's KP hierarchy
    • Singapore: World Scientific Publishing Company
    • Magnano, G., Magri, F.: Poisson-Nijenhuis structures, truncated loop algebras and Sato's KP hierarchy. In: Integrable systems and quantum groups. Singapore: World Scientific Publishing Company, 1992, pp. 147-172
    • (1992) Integrable Systems and Quantum Groups , pp. 147-172
    • Magnano, G.1    Magri, F.2
  • 34
    • 36749117832 scopus 로고
    • A simple model of an integrable Hamiltonian system
    • Magri, F.: A simple model of an integrable Hamiltonian system. J. Math. Phys. 19, 1156 -1162 (1978)
    • (1978) J. Math. Phys. , vol.19 , pp. 1156-1162
    • Magri, F.1
  • 35
    • 0000247924 scopus 로고
    • A geometrical approach to the nonlinear solvable equations
    • Nonlinear evolution equations and dynamical systems, M. Boiti, F. Pempinelli and G. Soliani (Eds.), Berlin, Heidelberg, New York: Springer
    • Magri, F.: A geometrical approach to the nonlinear solvable equations. In: Nonlinear evolution equations and dynamical systems, M. Boiti, F. Pempinelli and G. Soliani (Eds.), Lecture Notes in Physics, 120. Berlin, Heidelberg, New York: Springer, 1980, pp. 233-263
    • (1980) Lecture Notes in Physics , vol.120 , pp. 233-263
    • Magri, F.1
  • 36
    • 0003554962 scopus 로고
    • A geometrical characterization of integrable Hamiltonian systems through the theory of the poisson-nijenhuis manifolds
    • Universita di Milano
    • Magri, F., Morosi, C.: A geometrical characterization of integrable Hamiltonian systems through the theory of the Poisson-Nijenhuis manifolds. Quaderno S 19, Universita di Milano (1984)
    • (1984) Quaderno S , vol.19
    • Magri, F.1    Morosi, C.2
  • 37
    • 0000610551 scopus 로고
    • When do recursion operators generate new conservation laws?
    • Marmo, G., Vilasi, G.: When do recursion operators generate new conservation laws? Phys. Lett. B 277, 137-140 (1992)
    • (1992) Phys. Lett. B , vol.277 , pp. 137-140
    • Marmo, G.1    Vilasi, G.2
  • 38
    • 49549151837 scopus 로고
    • Reduction of symplectic manifolds with symmetry
    • Marsden, J., Weinstein, A.: Reduction of symplectic manifolds with symmetry. Rep. Math. Phys. 5, 121-130 (1974)
    • (1974) Rep. Math. Phys. , vol.5 , pp. 121-130
    • Marsden, J.1    Weinstein, A.2
  • 39
  • 40
    • 0002313312 scopus 로고
    • Compatible brackets in hamiltonian mechanics
    • A.S. Fokas, V.E. Zakharov (eds.). Berlin, Heidelberg, New York: Springer
    • McKean, H.P.: Compatible brackets in Hamiltonian mechanics. In: Important developments in soliton theory. A.S. Fokas, V.E. Zakharov (eds.). Berlin, Heidelberg, New York: Springer, 1993, pp. 344-354
    • (1993) Important Developments in Soliton Theory , pp. 344-354
    • McKean, H.P.1
  • 41
    • 3042570326 scopus 로고
    • Convergent series expansions for quasi-periodic motions
    • Moser, J.: Convergent series expansions for quasi-periodic motions. Math. Annalen 169, 136 -176 (1967)
    • (1967) Math. Annalen , vol.169 , pp. 136-176
    • Moser, J.1
  • 42
    • 0000234399 scopus 로고
    • Action-angle variables and their generalizations
    • Nekhoroshev, N.N.: Action-angle variables and their generalizations. Trans. Moscow Math. Soc. 26, 180-198 (1972)
    • (1972) Trans. Moscow Math. Soc. , vol.26 , pp. 180-198
    • Nekhoroshev, N.N.1
  • 43
    • 0001443815 scopus 로고
    • The poincaré-lyapunov-liouville-Arnol'd theorem
    • Nekhoroshev, N.N.: The Poincaré-Lyapunov-Liouville-Arnol'd Theorem. Funct. Anal. Appl. 28, 128-129 (1992)
    • (1992) Funct. Anal. Appl. , vol.28 , pp. 128-129
    • Nekhoroshev, N.N.1
  • 45
    • 0000842014 scopus 로고
    • Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems
    • Oevel, W., Zhang, H., Fuchssteiner, B.: Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems. Progr. Theor. Phys. 81, 294-308 (1989)
    • (1989) Progr. Theor. Phys. , vol.81 , pp. 294-308
    • Oevel, W.1    Zhang, H.2    Fuchssteiner, B.3
  • 46
    • 0040875591 scopus 로고
    • BiHamiltonian systems
    • B.D. Sleeman, R.J. Jarvis (eds.). New York: Longman Scientific and Technical
    • Olver, P.J.: BiHamiltonian systems. In: Pitman Research Notes in Mathematics Series 157. B.D. Sleeman, R.J. Jarvis (eds.). New York: Longman Scientific and Technical, 1987, pp. 176 -193
    • (1987) Pitman Research Notes in Mathematics Series , vol.157 , pp. 176-193
    • Olver, P.J.1
  • 47
    • 25044445587 scopus 로고
    • Canonical forms and integrability of bi-Hamiltonian systems
    • Olver, P.J.: Canonical forms and integrability of bi-Hamiltonian systems. Phys. Lett. A 148, 177-187 (1990)
    • (1990) Phys. Lett. A , vol.148 , pp. 177-187
    • Olver, P.J.1
  • 49
    • 0040281279 scopus 로고
    • A definition of the exterior derivative in terms of Lie derivatives
    • Palais, R.S.: A definition of the exterior derivative in terms of Lie derivatives. Proc. Amer. Math. Soc. 5, 902-908 (1954)
    • (1954) Proc. Amer. Math. Soc. , vol.5 , pp. 902-908
    • Palais, R.S.1
  • 53
    • 0001283472 scopus 로고
    • Classification locale d'un couple de formes symplectiques poisson-compatibles
    • S. I
    • Turiel, F.J.: Classification locale d'un couple de formes symplectiques Poisson-compatibles. C.R. Acad. Sci. Paris 308, S. I, 575-578 (1989)
    • (1989) C.R. Acad. Sci. Paris , vol.308 , pp. 575-578
    • Turiel, F.J.1
  • 54
    • 85080013909 scopus 로고
    • New aspects of complete integrability
    • Singapore: World Scientific Publishing Company
    • Vilasi, G.: New aspects of complete integrability. In: Integrable systems and quantum groups. Singapore: World Scientific Publishing Company, 1992, pp. 126-146
    • (1992) Integrable Systems and Quantum Groups , pp. 126-146
    • Vilasi, G.1
  • 55
    • 0039689511 scopus 로고
    • On the local structures of recursion operators for symmetries
    • Ten Eikelder, H.M.M.: On the local structures of recursion operators for symmetries. Proc. Kon. Ned. Akad. Amsterdam 89, 389-403 (1986)
    • (1986) Proc. Kon. Ned. Akad. Amsterdam , vol.89 , pp. 389-403
    • Ten Eikelder, H.M.M.1


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