Perturbed Hamiltonian Dynamics from Deformation of Poisson Brackets

M. Avendaño-Camacho; R. Flores-Espinoza; Yu Vorobiev

doi:10.1134/S106192081903004X

Perturbed Hamiltonian Dynamics from Deformation of Poisson Brackets

M. Avendaño-Camacho^*, R. Flores-Espinoza, Yu Vorobiev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In the context of normal forms, we study a class of perturbed Hamiltonian systems on phase spaces with symmetry which arise from deformation of Poisson brackets. By combining the averaging method with some facts on the Poisson invariant cohomology, we derive various normalization criteria. In particular, we compute the invariant normal forms of first order for systems of adiabatic type on Poisson fibrations by using the technique of Hannay-Berry connections.

Original language	English
Pages (from-to)	277-285
Number of pages	9
Journal	Russian Journal of Mathematical Physics
Volume	26
Issue number	3
DOIs	https://doi.org/10.1134/S106192081903004X
State	Published - 1 Jul 2019
Externally published	Yes

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© 2019, Pleiades Publishing, Ltd.

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10.1134/S106192081903004X

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AU - Vorobiev, Yu

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N2 - In the context of normal forms, we study a class of perturbed Hamiltonian systems on phase spaces with symmetry which arise from deformation of Poisson brackets. By combining the averaging method with some facts on the Poisson invariant cohomology, we derive various normalization criteria. In particular, we compute the invariant normal forms of first order for systems of adiabatic type on Poisson fibrations by using the technique of Hannay-Berry connections.

AB - In the context of normal forms, we study a class of perturbed Hamiltonian systems on phase spaces with symmetry which arise from deformation of Poisson brackets. By combining the averaging method with some facts on the Poisson invariant cohomology, we derive various normalization criteria. In particular, we compute the invariant normal forms of first order for systems of adiabatic type on Poisson fibrations by using the technique of Hannay-Berry connections.

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Perturbed Hamiltonian Dynamics from Deformation of Poisson Brackets

Abstract

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