Abstract
A remarkable map between the generalized Henon-Heiles system and the Garnier system is obtained by means of a detailed comparison between two finite-dimensional reduction methods for soliton equations: thestationary flows and therestricted flows. The role of the Gelfand-Dickey polynomials and of the KdV Poisson pencil in this construction is emphasized.
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References
A.P. Fordy, The Henon-Heiles system revisited Physica. 1991. V. 52D. P. 204–210.
C.W. Cao, Henan Science. 1987. V. 5. P. 1.
M. Antonowicz and S. Rauch-Wojciechowski, How to construct finite dimensional bi-Hamiltonian systems from soliton equations: Jacobi integrable potentials. J. Math. Phys. 1992. V. 33. P. 2115–2125.
L.A. Dickey, Soliton Equations and Hamiltonian Systems. Singapore: World Scientific, 1991.
M. Antonowicz and S. Rauch-Wojciechowski, Bi-Hamiltonian Formulation of the Henon-Heiles System and Its Multidimensional Extensions Phys. Lett. 1992 V. 163A. P. 167–172.
S. Wojciechowski, Integrability of one particle in a perturbed central quartic potential Physica Scripta. 1985. V. 31. P. 433–438.
P. Casati, F. Magri, and M. Pedroni, Bihamiltonian Manifolds and the τ-function//Contemporary Mathematics 132/ed. M. J. Gotay et al., Providence: American Mathematical Society. 1992. P. 213–234.
S. Rauch-Wojciechowski, Newton representation for stationary flows of the KdV hierarchy Phys. Lett. 1991. V. 170A. P. 91–94.
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Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Piaz.le Europa 1, I34127 Trieste, Italy. E-mail: tondo@univ.trieste.it. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 552–559, June, 1994.
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Tondo, G. A connection between the Henon-Heiles system and the Garnier system. Theor Math Phys 99, 796–802 (1994). https://doi.org/10.1007/BF01017070
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DOI: https://doi.org/10.1007/BF01017070