A constant of motion in 3D implies a local generalized Hamiltonian structure

We demonstrate that a Poisson structure can always be associated to a general nonautonomous 3D vector field of ODEs by means of a diffeomorphism that preserves both the orientation and the volume of phase-space. The only prerequisite is the existence of one constant of motion.

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Veröffentlicht in:	arXiv.org 2019-10
Hauptverfasser:	Hernández-Bermejo, Benito, Fairén, Victor
Format:	Artikel
Sprache:	eng
Schlagworte:	Fields (mathematics) Isomorphism Mathematics - Analysis of PDEs Mathematics - Dynamical Systems Mathematics - Mathematical Physics Physics - Classical Physics Physics - Exactly Solvable and Integrable Systems Physics - Mathematical Physics Three dimensional motion
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Beschreibung
Zusammenfassung:	We demonstrate that a Poisson structure can always be associated to a general nonautonomous 3D vector field of ODEs by means of a diffeomorphism that preserves both the orientation and the volume of phase-space. The only prerequisite is the existence of one constant of motion.
ISSN:	2331-8422
DOI:	10.48550/arxiv.1910.03888