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. 
@article{IVM_2011_9_a7,
     author = {A. K. Rybnikov},
     title = {Differential-geometric structures defining higher order contact transformations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {70--89},
     publisher = {mathdoc},
     number = {9},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_9_a7/}
}
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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/