Hamiltonian formalism for fiberwise linear dynamical systems

Ruben Flores Espinoza*, Yurii Vorobjev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the Hamiltonization problem for fiberwise linear dynamical systems on a vector bundle in a wide class of symplectic structures. Two types of results are presented: (i) a Hamiltonization criterion is formulated as the solvability of some differential equations on the base including a matrix equation of Lax's type; (ii) a geometric interpretation of these equations is given in terms of symplectic connections. We consider some examples where there are nontrivial obstructions to the existence of Hamiltonian structures for fiberwise linear dynamics.

Original languageEnglish
Pages (from-to)213-234
Number of pages22
JournalBoletin de la Sociedad Matematica Mexicana
Volume6
Issue number2
StatePublished - 2000

Keywords

  • Lax's equation
  • Proper Hamiltonian structures
  • Symplectic connections
  • Symplectic manifolds

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