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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 1, Pages 86–88
DOI: https://doi.org/10.26907/0021-3446-2019-1-86-88
(Mi ivm9425)
 

Brief communications

On classification of polynomial Hamiltonians with non-degenerated linear-stable singular point

P. V. Bibikov

Institute of Control Sciences of Russian Academy of Sceinces, 65 Profsoyuznaya str., Moscow, 117997 Russia
References:
Abstract: 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.
Keywords: hamiltonian, symplectomorphism, polynomial automorphism, Birkhoff normal form, Galois group.
Funding agency Grant number
Russian Foundation for Basic Research 16-31-60018_мол_а_дк
Supported by the Russian Foundation for Basic Research (Grant mol_a_dk No. 16-31-60018).
Received: 20.09.2018
Revised: 26.09.2018
Accepted: 20.09.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 1, Pages 76–78
DOI: https://doi.org/10.3103/S1066369X19010092
Bibliographic databases:
Document Type: Article
UDC: 514.164
Language: Russian
Citation: P. V. Bibikov, “On classification of polynomial Hamiltonians with non-degenerated linear-stable singular point”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 1, 86–88; Russian Math. (Iz. VUZ), 63:1 (2019), 76–78
Citation in format AMSBIB
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\paper On classification of polynomial Hamiltonians with non-degenerated linear-stable singular point
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\pages 86--88
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\jour Russian Math. (Iz. VUZ)
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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