Extended integrability and Bi-Hamiltonian systems

Communications in Mathematical Physics

Volumn 196, Issue 1, 1998, Pages 19-51

  Bogoyavlenskij, Oleg I ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032475009     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050412     Document Type: Article

References (34)

1. Abraham, R., Marsden, J. E.: Foundations of mechanics. London: The Benjamin/Cummings Publishing, 1978
2. Alfven, H., Falthammar, C.-G.: Cosmical electrodynamics. Fundamental principles. Oxford: Clarendon Press, 1963
3. Arnold, V. I., Avez, A.: Ergodic problems of classical mechanics. New York: W. A. Benjamin, Inc., 1968
4. Bogoyavlenskij, O. I.: On perturbations of the periodic Toda lattice. Commun. Math. Phys. 51, 201-209 (1976)
5. Bogoyavlenskij, O. I.: A concept of integrability of dynamical systems. Compt. Rend. Acad. Sci. Canada 18, 163-169 (1996)
6. Bogoyavlenskij, O. I.: An extended concept of integrability and its applications. I. Two topological invariants of integrable Hamiltonian systems. Preprint 1996-08. Kingston: Queen's University, 1996
7. Bogoyavlenskij, O. I.: Theory of tensor invariants of integrable Hamiltonian systems. I. Incompatible Poisson structures. Commun. Math. Phys. 180, 529-586 (1996)
8. Bogoyavlenskij, O. I.: Theory of tensor invariants of integrable Hamiltonian systems. II. Theorem on symmetries and its applications. Commun. Math. Phys. 184, 301-365 (1997)
9. Bogoyavlenskij, O. I.: Conformal symmetries of dynamical systems and Poincaré's 1892 concept of iso-energetic non-degeneracy. C. R. Acad. Sci. Paris, 326 S. I, 213-218 (1998)
10. Clemmow, P. C., Dougherty, J. P.: Electrodynamics of particles and plasmas. Reading, Massachusetts: Addison-Wesley Publishing Co., 1969
11. Duistermaat, J. J.: On global action-angle coordinates. Commun. Pure Appl. Math. 33, 687-706 (1980)
12. Fuchssteiner, B.: Applications of hereditary symmetries to nonlinear evolution equations. Nonlinear Analysis, Theory, Methods and Applic. 3, 849-862 (1979)
13. Gelfand, I. M., Dorfman, I. Ya.: Hamiltonian operators and algebraic structures related to them. Funct. Anal. Appl. 13, 248-262 (1979)
14. inf des orbites périodiques sur un ouvert de surfaces d'energies. C. R. Acad. Sci. Paris 312, S. 1, 989-994 (1991)
15. inf des orbites récurrentes de flots hamiltonians. C. R. Acad. Sci. Paris 313, S. I, 49-51 (1991)
16. Hofer, H., Zehnder, E.: Symplectic invariants and Hamiltonian dynamics. Basel: Birkhauser Verlag, 1994
17. Jost, R.: Winkel-und wirkungsvariable für allgemeine mechanische Systeme. Helvetica Physica Acta 41, 965-968 (1968)
18. 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
19. Liouville, J.: Note sur l'intégration des équations différentielles de la Dynamique. J. Math. Pures Appl. 20, 137-138 (1855)
20. Magri, F: A simple model of an integrable Hamiltonian system. J. Math. Phys. 19, 1156-1162 (1978)
21. Markus, L., Meyer, K. R.: Generic Hamiltonian dynamical systems are neither integrable nor ergodic. Memoirs of AMS, 144, 1974
22. Marsden, J.: Lectures on mechanics. Cambridge: Cambridge University Press, 1992
23. Meyer, K. R.: Hamiltonian systems with a discrete symmetry. J. Diff. Eqs. 41, 228-238 (1981)
24. Moser, J.: Old and new applications of KAM theory. NATO Conference "Hamiltonian systems of 3 and more degrees of freedom". Barcelona, August 1995
25. Nekhoroshev, N. N.: Action-angle variables and their generalizations. Trans. Moscow Math. Soc. 26, 180-198 (1972)
26. n-1-forming sets of eigenvectors. Proc. Kon. Ned. Akad. Amsterdam 54, 200-212 (1951)
27. Parasyuk, I. O.: Conservation of multidimensional invariant tori of Hamiltonian systems. Ukr. Math. J. 36, 380-385 (1984)
28. Parasyuk, I. O.: Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori. Ukr. Math. J. 45, 85-93 (1993)
29. Parasyuk, I. O.: Reduction and coisotropic invariant tori of Hamiltonian systems with non-Poisson commutative symmetries. I. II, Ukr. Math. J. 46, 572-580, 994-002 (1994)
30. Parasyuk, I. O.: Coisotropic invariant tori of Hamiltonian systems of the quasiclassical theory of motion of a conduction electron. Ukr. Math. J. 42, 308-312 (1990)
31. Poincaré, H.: Les métodes nouvelles de la mécanique céleste. T. 1. Paris: Gauthier-Villars, 1892
32. Zehnder, E.: Remarks on periodic solutions on hypersurfaces. In: Periodic solutions of Hamiltonian systems and related topics. P. H. Rabinowitz (Ed.). Dordrecht: D. Reidel Publ. Co., 1987, pp. 267-279
33. Novikov, S.P.: The Hamiltonian formalism and a multi-valued analogue of Morse theory. Russ. Math. Surv. 37 (5), 1-56 (1982)
34. Arnold, V.I.: Sur la topologie des écoulements stationnaires des fluides parfaits. C. R. Acad. Sci. Paris, 261 S. I, 17-20 (1965)