Contact Lie systems
Abstract
We define and analyse the properties of contact Lie systems, namely systems of first-order differential equations describing the integral curves of a -dependent vector field taking values in a finite-dimensional Lie algebra of Hamiltonian vector fields relative to a contact structure. As a particular example, we study families of conservative contact Lie systems. Liouville theorems, contact reductions, and Gromov non-squeezing theorems are developed and applied to contact Lie systems. Our results are illustrated by examples with relevant physical and mathematical applications, e.g. Schwarz equations, Brockett systems, etcetera.
Cite
@article{arxiv.2207.04038,
title = {Contact Lie systems},
author = {Javier de Lucas and Xavier Rivas},
journal= {arXiv preprint arXiv:2207.04038},
year = {2023}
}
Comments
29 pp, 4 figures. New version of the manuscript with Sections 4, 5.4, and 6 added. Many new results included and typos corrected