Abstract
For Toda lattices, properties of the canonical transformations of the extended phase space that preserve integrability are considered. It is proved that these transformations change the Lax matrices, r-matrix relations, the Bäcklund transformations, the action-angles variables but preserve the separated variables and basic characteristics of the corresponding spectral curves. Bibliography: 15 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, 2nd edition (1989).
A. V. Bolsinov, V. V. Kozlov, and A. T. Fomenko, Usp. Mat. Nauk, 50, No. 3, 4–31 (1994).
K. Jacobi, Lectures in Dynamics1842–1843 [Russian translation], Leningrad (1936).
H. Flaschka and D. Mc. Laughlin, Prog. Theor. Phys., 55, 438(1976).
M. Gaudin, La Fonction d'Onde de Bethe, Masson, Paris (1983).
L. A. Takhtajan and L. D. Faddeev, Hamiltonian Approach to the Theory of Solitons[in Russian], Moscow (1986).
M. Kac and P. Van Moerbeke, Proc. Nat. Acad. Sci. USA, 72, 1627, 2879(1975).
C. Lanczos, The Variational Principles of Mechanics, Toronto (1949).
L. D. Landau and E. M. Lifshits, Mechanics(1958).
S. P. Novikov, Usp. Mat. Nauk, 37, No. 5, 3–49 (1982).
V. Pasquier and M. Gaudin, J. Phys. A., 25, 5243(1992).
E. K. Sklyanin, Lect. Notes Phys., 226, 196(1985).
E. K. Sklyanin and V. B. Kuznetsov, J. Phys., 31, 2241(1998).
A. V. Tsiganov, Teor. Math. Phys., 120, 27(1999).
A. V. Tsiganov, "Canonical transformations of the extended phase, Toda lattices and St¨ ackel family of inte-grable systems," Preprint solv-int/9909006 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tsiganov, A.V. The Maupertuis-Jacobi Transformations and Toda Chains. Journal of Mathematical Sciences 115, 2085–2091 (2003). https://doi.org/10.1023/A:1022620401099
Issue Date:
DOI: https://doi.org/10.1023/A:1022620401099