Geodesic
Bi-Hamiltonian systems of natural form
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 161-182 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We propose a new method for constructing integrable systems of natural form. In this method, integrals of motion are solutions of an overdetermined system of algebraic and partial differential equations obtained from the compatibility condition for Poisson tensors polynomial in the momenta and from the condition that the bi-Lagrangian distribution corresponding to the integrals of motion is invariant under the action of the recursion operator.
Keywords: integrable system, bi-Hamiltonian manifold, separation of variables. 
@article{TMF_2006_149_2_a1,
     author = {A. V. Tsiganov},
     title = {Bi-Hamiltonian systems of natural form},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {161--182},
     year = {2006},
     volume = {149},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a1/}
}
TY  - JOUR
AU  - A. V. Tsiganov
TI  - Bi-Hamiltonian systems of natural form
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 161
EP  - 182
VL  - 149
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a1/
LA  - ru
ID  - TMF_2006_149_2_a1
ER  - 
%0 Journal Article
%A A. V. Tsiganov
%T Bi-Hamiltonian systems of natural form
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 161-182
%V 149
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a1/
%G ru
%F TMF_2006_149_2_a1
A. V. Tsiganov. Bi-Hamiltonian systems of natural form. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 161-182. http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a1/

[1] F. Magri, “Eight lectures on integrable systems”, Integrability of Nonlinear Systems, Proc. of the CIMPA school (Pondicherry Univ., India, January 8–25, 1996), Lect. Notes Phys., 495, eds. Y. Kosmann-Schwarzbach et al., Springer, Berlin–Heidelberg, 1997, 256–296 | DOI | MR | Zbl

[2] J. Hietarinta, Phys. Rep., 147 (1987), 87–154 | DOI | MR

[3] G. Falqui, F. Magri, M. Pedroni, J. Nonlinear Math. Phys., 8 (2001), 118–127 | DOI | MR | Zbl

[4] G. Falqui, M. Pedroni, Math. Phys. Anal. Geom., 6 (2003), 139–179 | DOI | MR | Zbl

[5] Y. Kosmann-Schwarzbach, F. Magri, Ann. Inst. H. Poincaré, Phys. Théor., 53 (1990), 35–81 | MR | Zbl

[6] B. Fuchssteiner, A. Fokas, Physica D, 4 (1981), 47–66 | DOI | MR | Zbl

[7] I. M. Gelfand, I. Ya. Dorfman, Funkts. analiz i ego prilozh., 13:4 (1979), 13–30 | MR | Zbl

[8] R. Brouzet, J. Math. Phys., 34 (1993), 1309–1313 | DOI | MR | Zbl

[9] A. M. Perelomov, Integriruemye sistemy klassicheskoi mekhaniki i algebry Li, Nauka, M., 1990 | MR | Zbl

[10] C. Bartocci, G. Falqui, M. Pedroni, Differ. Geom. Appl., 21:3 (2004), 349–360 | DOI | MR | Zbl

[11] A. V. Tsiganov, Yu. A. Grigoryev, Regul. Chaotic Dyn., 10 (2005), 413–422 | DOI | MR

[12] A. Ibort, F. Magri, G. Marmo, J. Geom. Phys., 33 (2000), 210–228 | DOI | MR | Zbl

[13] A. V. Tsiganov, J. Math. Phys., 40 (1999), 279–298 | DOI | MR | Zbl

[14] S. Benenti, J. Math. Phys., 38 (1997), 6578–6602 | DOI | MR | Zbl

[15] P. A. Damianou, Rev. Math. Phys., 16 (2004), 175–241 | DOI | MR | Zbl

[16] R. L. Fernandes, J. Phys. A, 26 (1993), 3797–3803 | DOI | MR | Zbl

[17] V. I. Inozemtsev, Commun. Math. Phys., 121 (1989), 629–643 | DOI | MR | Zbl

[18] C. R. Holt, J. Math. Phys., 23 (1982), 1037–1046 | DOI | MR | Zbl

[19] J. Drach, C. R. Acad. Sci. Paris, 200 (1935), 22–26 | Zbl

[20] A. V. Tsyganov, TMF, 124:3 (2000), 426–444 | DOI | MR | Zbl

[21] S. Rauch-Wojciechowski, A. V. Tsiganov, J. Phys. A, 29 (1996), 7769–7778 | DOI | MR | Zbl

[22] M. Wojciechowska, S. Wojciechowski, Phys. Lett. A, 105 (1984), 11–14 | DOI | MR