Infinitesimal Poisson algebras and linearization of Hamiltonian systems

J. C. Ruíz-Pantaleón; D. García-Beltrán; Yu Vorobiev

doi:10.1007/s10455-020-09733-6

Infinitesimal Poisson algebras and linearization of Hamiltonian systems

J. C. Ruíz-Pantaleón^*, D. García-Beltrán, Yu Vorobiev

^*Autor correspondiente de este trabajo

Resultado de la investigación: Contribución a una revista › Artículo › revisión exhaustiva

1 Cita (Scopus)

Resumen

Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides a suitable framework for the study of the Hamiltonization problem for the linearized dynamics along Poisson submanifolds.

Idioma original	Inglés
Páginas (desde-hasta)	415-431
Número de páginas	17
Publicación	Annals of Global Analysis and Geometry
Volumen	58
N.º	4
DOI	https://doi.org/10.1007/s10455-020-09733-6
Estado	Publicada - 1 nov 2020

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© 2020, Springer Nature B.V.

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author = "Ru{\'i}z-Pantale{\'o}n, {J. C.} and D. Garc{\'i}a-Beltr{\'a}n and Yu Vorobiev",

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AU - Ruíz-Pantaleón, J. C.

AU - García-Beltrán, D.

AU - Vorobiev, Yu

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Y1 - 2020/11/1

N2 - Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides a suitable framework for the study of the Hamiltonization problem for the linearized dynamics along Poisson submanifolds.

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KW - Hamiltonian system

KW - Linearization

KW - Poisson algebra

KW - Poisson submanifold

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Infinitesimal Poisson algebras and linearization of Hamiltonian systems

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