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Russian Mathematics

, Volume 63, Issue 1, pp 76–78 | Cite as

On Classification of Polynomial Hamiltonians With Nondegenerate Linearly Stable Singular Point

  • P. V. BibikovEmail author
Brief communications

Abstract

We study the problem of classification of polynomial Hamiltonians with a non-degenerate linearly stable singular point on the two-dimensional complex plane with respect to the action of the group of polynomial symplectic automorphisms. To each Hamiltonian one can associate the set of polynomials in three variables which are the components of the Birkhoff normal form of the Hamiltonian and a finite group which is the Galois group of a finite-dimensional extension of the fields generated by the polynomials. Using these objects we provide an equivalence criterion for two polynomial Hamiltonians.

Key words

Hamiltonian symplectomorphism polynomial automorphism Birkhoff normal form Galois group 

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Notes

Acknowledgments

Supported by the Russian Foundation for Basic Research (Grant mol_a_dk No. 16-31-60018).

References

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Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Institute of Control Sciences of Russian Academy of SceincesMoscowRussia

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