Geodesic
On classification of polynomial Hamiltonians with non-degenerated linear-stable singular point
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 86-88.

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

We study the classification of polynomial Hamiltonians with the non-degenerated linear-stable singular point on the two-dimensional complex plane with respect to the action of the group of polynomial symplectic automorphisms. For each Hamiltonian one can associate the set of polynomials in three variables and the finite group. These variables are the components of the Birkhoff normal form of our Hamiltonian, and this group is the Galois group of the finite-dimensional extension of the fields, which is generated by our polynomials. Using these objects we provide the equivalence criterion for two polynomial Hamiltonians.
Mots-clés : hamiltonian, symplectomorphism, polynomial automorphism, Birkhoff normal form, Galois group. 
@article{IVM_2019_1_a8,
     author = {P. V. Bibikov},
     title = {On classification of polynomial {Hamiltonians} with non-degenerated linear-stable singular point},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--88},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {https://geodesic-test.mathdoc.fr/item/IVM_2019_1_a8/}
}
TY  - JOUR
AU  - P. V. Bibikov
TI  - On classification of polynomial Hamiltonians with non-degenerated linear-stable singular point
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2019
SP  - 86
EP  - 88
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/IVM_2019_1_a8/
LA  - ru
ID  - IVM_2019_1_a8
ER  - 
%0 Journal Article
%A P. V. Bibikov
%T On classification of polynomial Hamiltonians with non-degenerated linear-stable singular point
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2019
%P 86-88
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/IVM_2019_1_a8/
%G ru
%F IVM_2019_1_a8
P. V. Bibikov. On classification of polynomial Hamiltonians with non-degenerated linear-stable singular point. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 86-88. https://geodesic-test.mathdoc.fr/item/IVM_2019_1_a8/

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

[2] Kruglikov B., Lychagin V., “Global Lie–Tresse theorem”, Select. Math., New Ser., 22:3 (2016) | DOI | MR | Zbl

[3] Birkhoff G. D., Dynamical systems, Amer. Math. Soc. Colloqium Publ., IX, Amer. Math. Soc., 1927 | MR | Zbl

[4] Arzhantsev I., Flener H., Kaliman S., Kutzshebauch F., Zaidenberg M., Infinite transivity in affine varieties, arXiv: 1210.6937