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arXiv · 1412.0300

Jacobi-Lie systems: Fundamentals and low-dimensional classification

F. J. Herranz·J. de Lucas·C. Sardon
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Abstract

A Lie system is a system of differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields, a Vessiot-Guldberg Lie algebra. We define and analyze Lie systems possessing a Vessiot-Guldberg Lie algebra of Hamiltonian vector fields relative to a Jacobi manifold, the hereafter called Jacobi-Lie systems. We classify Jacobi-Lie systems on $\mathbb{R}$ and $\mathbb{R}^2$. Our results shall be illustrated through examples of physical and mathematical interest.

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BibTeXRIS

F. J. Herranz, J. de Lucas, C. Sardon. 2014-11-30. Jacobi-Lie systems: Fundamentals and low-dimensional classification. https://doi.org/10.3934/proc.2015.0605

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