Contact Lie systems
Abstract
We define and analyse the properties of contact Lie systems, namely systems of firstorder differential equations describing the integral curves of a $t$dependent vector field taking values in a finitedimensional 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 nonsqueezing 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2022
 arXiv:
 arXiv:2207.04038
 Bibcode:
 2022arXiv220704038D
 Keywords:

 Mathematical Physics;
 Mathematics  Differential Geometry;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 37J55;
 53D10;
 53Z05;
 34A26;
 34A05;
 34A34;
 17B66;
 22E70
 EPrint:
 18 pp