# American Institute of Mathematical Sciences

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2015, 2015(special): 605-614. doi: 10.3934/proc.2015.0605

## Jacobi--Lie systems: Fundamentals and low-dimensional classification

 1 Department of Physics, University of Burgos, 09001, Burgos, Spain 2 Department of Mathematical Methods in Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warszawa, Poland 3 Department of Fundamental Physics, University of Salamanca, Plza. de la Merced s/n, 37.008, Salamanca, Spain

Received  September 2014 Revised  March 2015 Published  November 2015

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.
Citation: F.J. Herranz, J. de Lucas, C. Sardón. Jacobi--Lie systems: Fundamentals and low-dimensional classification. Conference Publications, 2015, 2015 (special) : 605-614. doi: 10.3934/proc.2015.0605
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