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Lax Representations for Separable Systems from Benenti Class
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we construct Lax pairs for Stäckel systems with separation curves from so-called Benenti class. For each system of considered family we present an infinite family of Lax representations, parameterized by smooth functions of spectral parameter.
Keywords: Lax representation, Stäckel system, Benenti system, Hamiltonian mechanics. 
@article{SIGMA_2019_15_a44,
     author = {Maciej B{\l}aszak and Ziemowit Doma\'nski},
     title = {Lax {Representations} for {Separable} {Systems} from {Benenti} {Class}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2019},
     volume = {15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a44/}
}
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Maciej Błaszak; Ziemowit Domański. Lax Representations for Separable Systems from Benenti Class. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a44/

[1] Benenti S., “Inertia tensors and Stäckel systems in the Euclidean spaces”, Rend. Sem. Mat. Univ. Politec. Torino, 50 (1992), 315–341 | MR | Zbl

[2] Benenti S., “Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation”, J. Math. Phys., 38 (1997), 6578–6602 | DOI | MR | Zbl

[3] Benenti S., “Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems”, Acta Appl. Math., 87 (2005), 33–91 | DOI | MR | Zbl

[4] Błaszak M., “Separable systems with quadratic in momenta first integrals”, J. Phys. A: Math. Gen., 38 (2005), 1667–1685, arXiv: nlin.SI/0312025 | DOI | MR

[5] Błaszak M., “Non-autonomous Hénon–Heiles system from Painlevé class”, Phys. Lett. A, 383 (2019), 2149–2152, arXiv: 1904.05203 | DOI | MR

[6] Błaszak M., Sergyeyev A., “Natural coordinates for a class of Benenti systems”, Phys. Lett. A, 365 (2007), 28–33, arXiv: nlin.SI/0604022 | DOI | MR

[7] Błaszak M., Sergyeyev A., “Generalized Stäckel systems”, Phys. Lett. A, 375 (2011), 2617–2623 | DOI | MR

[8] Eilbeck J. C., Enol'skii V. Z., Kuznetsov V. B., Tsiganov A. V., “Linear $r$-matrix algebra for classical separable systems”, J. Phys. A: Math. Gen., 27 (1994), 567–578, arXiv: hep-th/9306155 | DOI | MR | Zbl

[9] Marciniak K., Błaszak M., “Flat coordinates of flat Stäckel systems”, Appl. Math. Comput., 268 (2015), 706–716, arXiv: 1406.2117 | DOI | MR | Zbl

[10] Mumford D., Tata lectures on theta. II, Progress in Mathematics, 43, Birkhäuser Boston, Inc., Boston, MA, 1984 | DOI | MR | Zbl

[11] Rauch-Wojciechowski S., Marciniak K., Błaszak M., “Two Newton decompositions of stationary flows of KdV and Harry Dym hierarchies”, Phys. A, 233 (1996), 307–330 | DOI | MR

[12] Ravoson V., Gavrilov L., Caboz R., “Separability and Lax pairs for Hénon–Heiles system”, J. Math. Phys., 34 (1993), 2385–2393 | DOI | MR | Zbl

[13] Tsiganov A. V., “Duality between integrable Stäckel systems”, J. Phys. A: Math. Gen., 32 (1999), 7965–7982, arXiv: solv-int/9812001 | DOI | MR | Zbl

[14] Vanhaecke P., Integrable systems in the realm of algebraic geometry, Lecture Notes in Math., 1638, 2nd ed., Springer-Verlag, Berlin, 2001 | DOI | MR | Zbl