Geodesic
Differential-geometric structures defining higher order contact transformations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 70-89.

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The paper is devoted to the study of differential-geometric structures generated by Lie–Bäcklund transformations (or, what is the same, higher order contact transformations), which are a special case of diffeomorphisms between two manifolds of holonomic jets of sections. We study the structure of the fundamental object of a second order contact diffeomorphism (2-diffeomorphism). We also consider the case when a 2-diffeomorphism is given by explicit equations connecting local coordinates of 2-jet manifolds and establish conditions under which 2-diffeomorphisms defined by explicit equations are contact diffeomorphisms.
Mots-clés : contact transformations
Keywords: Lie–Bäcklund transformations, fundamental objects of a differential-geometric structure. 
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     title = {Differential-geometric structures defining higher order contact transformations},
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A. K. Rybnikov. Differential-geometric structures defining higher order contact transformations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 70-89. http://geodesic.mathdoc.fr/item/IVM_2011_9_a7/

[1] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983

[2] Laptev G. F., “Invariant analytic theory of differentiable maps”, Oeuvres du Congrès International des Mathématiciens (Nice, 1970), Nice, 1970, 84–85

[3] Laptev G. F., “K invariantnoi teorii differentsiruemykh otobrazhenii”, Tr. Geometrich. semin., 6, VINITI, M., 1974, 37–42 | MR | Zbl

[4] Rybnikov A. K., “Differentsialno-geometricheskie struktury, opredelyayuschie preobrazovaniya Li–Beklunda”, Dokl. RAN, 425:1 (2009), 25–30 | Zbl

[5] Evtushik L. E., Lumiste Yu. G., Ostianu N. M., Shirokov A. P., “Differentsialno-geometricheskie struktury na mnogoobraziyakh”, Itogi nauki i tekhn. Probl. geometrii, 9, VINITI, M., 1979, 5–246 | MR | Zbl

[6] Laptev G. F., “Differentsialnaya geometriya pogruzhennykh mnogoobrazii. Teoretiko-gruppovoi metod differentsialno-geometricheskikh issledovanii”, Tr. Mosk. matem. o-va, 2 (1953), 275–382 | MR | Zbl

[7] Laptev G. F., “Teoretiko-gruppovoi metod differentsialno-geometricheskikh issledovanii”, Tr. 3-go Vsesoyuzn. matem. s'ezda (Moskva, 1956), v. 3, AN SSSR, M., 1958, 409–418

[8] Laptev G. F., “Osnovnye infinitezimalnye struktury vysshikh poryadkov na gladkom mnogoobrazii”, Tr. Geometrich. semin., 1, VINITI, M., 1966, 139–189 | MR | Zbl

[9] Laptev G. F., “Strukturnye uravneniya glavnogo rassloennogo mnogoobraziya”, Tr. Geometrich. semin., 2, VINITI, M., 1969, 161–178 | MR | Zbl

[10] Vasilev A. M., Teoriya differentsialno-geometricheskikh struktur, Izd-vo MGU, M., 1987

[11] Polyanin L. D., Zaitsev V. F., Zhurov A. I., Metody resheniya nelineinykh uravnenii matematicheskoi fiziki i mekhaniki, Fizmatlit, M., 2005