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

^*Corresponding author for this work

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

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	415-431
Number of pages	17
Journal	Annals of Global Analysis and Geometry
Volume	58
Issue number	4
DOIs	https://doi.org/10.1007/s10455-020-09733-6
State	Published - 1 Nov 2020

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Publisher Copyright:
© 2020, Springer Nature B.V.

Keywords

Contravariant derivative
Hamiltonian system
Linearization
Poisson algebra
Poisson submanifold

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10.1007/s10455-020-09733-6

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abstract = "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

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KW - Poisson submanifold

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Infinitesimal Poisson algebras and linearization of Hamiltonian systems

Abstract

Bibliographical note

Keywords

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