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.
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Acknowledgement
The authors are very grateful to José C. Ruíz-Pantaleón for fruitful discussions. This research was partially supported by CONACYT under the grants CB2013 no. 219631 and CB2015 no. 258302.
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To the memory of Mikhail Karasev
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Avendaño-Camacho, M., Flores-Espinoza, R. & Vorobiev, Y. Perturbed Hamiltonian Dynamics from Deformation of Poisson Brackets. Russ. J. Math. Phys. 26, 277–285 (2019). https://doi.org/10.1134/S106192081903004X
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DOI: https://doi.org/10.1134/S106192081903004X