Geodesic
On the subgroups of birational contact maps and the Kartan--Keller's conjecture
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 9-17.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present paper the new approach to description of contact birational maps of 1-jet space is suggested. This approach is based on the notion of symplectization of the 1-jet space. 
@article{DVMG_2018_18_1_a1,
     author = {P. V. Bibikov},
     title = {On the subgroups of birational contact maps and the {Kartan--Keller's} conjecture},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {9--17},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a1/}
}
TY  - JOUR
AU  - P. V. Bibikov
TI  - On the subgroups of birational contact maps and the Kartan--Keller's conjecture
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2018
SP  - 9
EP  - 17
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a1/
LA  - ru
ID  - DVMG_2018_18_1_a1
ER  - 
%0 Journal Article
%A P. V. Bibikov
%T On the subgroups of birational contact maps and the Kartan--Keller's conjecture
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2018
%P 9-17
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a1/
%G ru
%F DVMG_2018_18_1_a1
P. V. Bibikov. On the subgroups of birational contact maps and the Kartan--Keller's conjecture. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 9-17. http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a1/

[1] B. Kriglikov, V. Lychagin, “Global Lie-Tresse theorem”, Selecta Mathematica, New Series, 22:3 (2016), 1357–1411 | DOI | MR

[2] P. Bibikov, V. Lychagin, “$\mathrm{GL}_2(\mathbb{C})$-orbits of binary rational forms”, Lobachevskii Journal of Mathematics, 32:1 (2011), 95–102 | DOI | MR | Zbl

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

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

[5] P. Bibikov, V. Lychagin, “On differential invariants of actions of semisimple Lie groups”, J. Geometry and Physics, 2014, no. 85, 99–105 | DOI | MR | Zbl

[6] P. Bibikov, V. Lychagin, “Differential Contra Algebraic Invariants: Applications to Classical Algebraic Problems”, Lobachevskii Journal of Mathematics, 37:1 (2016), 36–49 | DOI | MR | Zbl

[7] P. Bibikov, “Zadacha Li i differentsialnye invarianty ODU vida $y'' = F(x,y)$”, Funktsionalnyi analiz i ego prilozheniya, 51:4 (2017) | DOI | MR | Zbl

[8] P. Bibikov, “Generalized Lie Problem and Differential Invariants for the Third Order ODEs”, Lobachevskii Journal of Mathematics, 38:4 (2017), 622–629 | DOI | MR | Zbl

[9] P. Bibikov, A. Malakhov, “On Lie problem and differential invariants for the subgroup of the plane Cremona group”, Journal of Geometry and Physics, 2017, no. 121, 72–82 | DOI | MR | Zbl

[10] E. Ferapontov, M. Pavlov, R. Vitolo, “Towards the Classification of Homogeneous Third-Order Hamiltonian Operators”, International Mathematics Research Notices, 2016:22 (2016), 6829-6855 | MR

[11] Yu. Galitski, D. Timashev, “On classification of metabelian Lie algebras”, Journal of Lie Theory, 9:1 (1999), 125–156 | MR | Zbl

[12] D. Alekseevskii, A. Vinogradov, V. Lychagin, “Osnovnye idei i ponyatiya differentsialnoi geometrii”, Geometriya – 1, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 28, VINITI, M., 1988, 5–289

[13] P. Bibikov, “Differential Invariants and Contact Classification of Ordinary Differential Equations”, Lobachevskii Journal of Mathematics, 36:3 (2015), 245–249 | DOI | MR | Zbl

[14] F. Klein, Vorlesungen über höhere Geometrie, Springer, Berlin, 1926 | MR | Zbl

[15] O. Keller, “Zur Theorie der ebenen Berührungstransformationen I”, Math. Ann., 120 (1947), 650–675 | DOI | MR

[16] M. Gizatullin, “Klein’s conjecture for contact automorphisms of the three-dimensional affine space”, Michigan Math. J., 2008, no. 58, 89–98 | DOI | MR | Zbl

[17] V. Iskovskikh, “Obrazuyuschie v dvumernoi gruppe Kremony nad nezamknutym polem”, Teoriya chisel, algebra, matematicheskii analiz i ikh prilozheniya, Sb. st. Posvyaschaetsya 100-letiyu so dnya rozhdeniya Ivana Matveevicha Vinogradova, Tr. MIAN, 200, Nauka, M., 1991, 157–170

[18] V. Arnold, Matematicheskie metody v klassicheskoi mekhanike, Nauka, M., 1989 | MR

[19] V. Popov, “Algebraic groups and the Cremona group”, Oberwolfach Reports, 10:2 (2013), 1053–1055

[20] P. Bibikov, “On symplectization of 1-jet space and differential invariants of point pseudogroup”, J. Geometry and Physics, 2014, no. 85, 81–87 | DOI | MR | Zbl