Geodesic
Classification of rational functions in symplectic and metric spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 3-9 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider symplectic and orthogonal classifications of rational functions of many variables. The main idea of these classifications consists in the use of methods of the differential geometry and the geometric theory of jet spaces. Namely, we consider group actions on an infinite jet space (rather than on functions), which allows us to find fields of differential invariants of these groups. Finally, we prove that dependencies between basic differential invariants and their derivatives completely determine the orbit of the corresponding function.
Keywords: symplectic group, rational function, differential invariant.
Mots-clés : orthogonal group, jet space 
@article{IVM_2013_4_a0,
     author = {P. V. Bibikov},
     title = {Classification of rational functions in symplectic and metric spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--9},
     year = {2013},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_4_a0/}
}
TY  - JOUR
AU  - P. V. Bibikov
TI  - Classification of rational functions in symplectic and metric spaces
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 3
EP  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_4_a0/
LA  - ru
ID  - IVM_2013_4_a0
ER  - 
%0 Journal Article
%A P. V. Bibikov
%T Classification of rational functions in symplectic and metric spaces
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 3-9
%N 4
%U http://geodesic.mathdoc.fr/item/IVM_2013_4_a0/
%G ru
%F IVM_2013_4_a0
P. V. Bibikov. Classification of rational functions in symplectic and metric spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2013_4_a0/

[1] Vinberg E. B., Popov V. L., “Teoriya invariantov”, Itogi nauki i tekhn. Ser. Sovremen. probl. matem. Fundam. napravleniya, 55, VINITI, M., 1989, 137–309 | MR | Zbl

[2] Bibikov P. V., Lychagin V. V., “$\mathrm{GL}_2(\mathbb C)$-orbity binarnykh form”, Dokl. RAN, 435:4 (2010), 439–440 | Zbl

[3] Bibikov P. V., Lychagin V. V., “$\mathrm{GL}_3(\mathbb C)$-orbity ratsionalnykh ternarnykh form”, Dokl. RAN, 438:4 (2011), 295–297 | MR

[4] Bibikov P. V., “Klassifikatsiya ternarnykh form s nulevym gessianom”, Izv. vuzov. Matem., 2011, no. 9, 99–101 | MR | Zbl

[5] Bibikov P. V., “Metricheskaya klassifikatsiya algebraicheskikh proektivnykh krivykh”, Izv. PGPU im. V. G. Belinskogo, 2011, no. 26, 36–42

[6] Bibikov P. V., Lychagin V. V., “Klassifikatsiya lineinykh deistvii algebraicheskikh grupp na prostranstvakh odnorodnykh form”, Dokl. RAN, 442:6 (2012), 732–735 | MR | Zbl

[7] Bibikov P. V., “On affine classification of functions and foliations on the plane”, Lobachevskii J. Math., 33:2 (2012), 115–122 | DOI | MR | Zbl

[8] Alekseevskii D. V., Vinogradov A. M., Lychagin V. V., “Osnovnye idei i ponyatiya differentsialnoi geometrii”, Itogi nauki i tekhn. Ser. Sovremen. probl. matem. Fundam. napravleniya, 28, VINITI, M., 1988, 5–289 | MR | Zbl

[9] Rosenlicht M., “Some basic theorems on algebraic groups”, Amer. J. Math., 78 (1956), 401–443 | DOI | MR | Zbl

[10] Vinberg E. B., Onischik A. L., Seminar po gruppam Li i algebraicheskim gruppam, URSS, M., 1995 | MR | Zbl