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Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems

CONACYT Research Fellow-Departamento de Matemáticas, Universidad de Sonora, Blvd. L. Encinas y Rosales s/n Col. Centro, C. P. 83000, Hermosillo, Sonora, México

E-mail Address: misaelave@mat.uson.mx

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and

Yury Vorobiev

Departamento de Matemáticas, Universidad de Sonora, Blvd. L. Encinas y Rosales s/n Col. Centro, C. P. 83000, Hermosillo, Sonora, México

E-mail Address: yurimv@guaymas.uson.mx

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https://doi.org/10.1142/S0219887817500864Cited by:7 (Source: Crossref)

Abstract

In the context of normal forms, we study a class of slow–fast Hamiltonian systems on general Poisson fiber bundles with symmetry. Our geometric approach is motivated by a link between the deformation theory for Poisson structures on fibered manifolds and the adiabatic perturbation theory. We present some normalization results which are based on the averaging theorem for horizontal 2-cocycles on Poisson fiber bundles.

Keywords:

AMSC: 53D19, 70G45, 70H09

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