Lie group foliations: Dynamical systems and integrators
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Differential Geometry
Dynamical Systems
Abstract
Foliate systems are those which preserve some (possibly singular) foliation of phase space, such as systems with integrals, systems with continuous symmetries, and skew product systems. We study numerical integrators which also preserve the foliation. The case in which the foliation is given by the orbits of an action of a Lie group has a particularly nice structure, which we study in detail, giving conditions under which all foliate vector fields can be written as the sum of a vector field tangent to the orbits and a vector field invariant under the group action. This allows the application of many techniques of geometric integration, including splitting methods and Lie group integrators.
Cite
@article{arxiv.math/0209387,
title = {Lie group foliations: Dynamical systems and integrators},
author = {Robert I. McLachlan and Matthew Perlmutter and G. Reinout W. Quispel},
journal= {arXiv preprint arXiv:math/0209387},
year = {2025}
}
Comments
20 pages