Geodesic
A connection between the Henon–Heiles system and the Garnier system
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 552-559 
G. Tondo. A connection between the Henon–Heiles system and the Garnier system. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 552-559. http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a25/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A remarkable map between a 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: the stationary flows and the restricted flows. The role of the Gelfand–Dickey polynomials and of the KdV Poisson pencil in this construction is emphasized.

[1] A. P. Fordy, “The Henon–Heiles system revisited”, Physica D, 52 (1991), 204–210 | DOI | MR | Zbl

[2] C. W. Cao, Henan Science, 5 (1987), 1 | MR | Zbl

[3] M. Antonowicz, S. Rauch-Wojciechowski, “How to construct finite dimensional bi-Hamiltonian systems from soliton equations: Jacobi integrable potentials”, J. Math. Phys., 33 (1992), 2115–2125 | DOI | MR | Zbl

[4] L. A. Dickey, Soliton Equations and Hamiltonian Systems, World Scientific, Singapore, 1991 | MR | Zbl

[5] M. Antonowicz, S. Rauch-Wojciechowski, “Bi-Hamiltonian Formulation of the Henon–Heiles System and its Multidimensional Extensions”, Phys. Lett. A, 163 (1992), 167–172 | DOI | MR

[6] S. Wojciechowski, “Integrability of One Particle in a Perturbed Central Quartic Potential”, Physica Scripta, 31 (1985), 433–438 | DOI | MR | Zbl

[7] P. Casati, F. Magri, M. Pedroni, “Bihamiltonian Manifolds and $\tau$-function”, Contemporary Mathematics, v. 132, eds. M. J. Gotay et al., American Mathematical Society, Providence, 1992, 213–234 | DOI | MR

[8] S. Rauch-Wojciechowski, “Newton representation for stationary flows of the KdV hierarchy”, Phys. Lett. A, 170 (1991), 91–94 | DOI | MR