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 journalArticlepeer-review

1 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 languageEnglish
Pages (from-to)415-431
Number of pages17
JournalAnnals of Global Analysis and Geometry
Volume58
Issue number4
DOIs
StatePublished - 1 Nov 2020

Bibliographical note

Funding Information:
This work was partially supported by the Mexican National Council of Science and Technology (CONACyT) under research project CB-258302. J. C. R.-P wishes also to thank CONACyT for the postdoctoral fellowship. The authors are very grateful to an anonymous Referee for critical comments and useful observations.

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

Keywords

  • Contravariant derivative
  • Hamiltonian system
  • Linearization
  • Poisson algebra
  • Poisson submanifold

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