Symplectic Groupoids for Poisson Integrators
Differential Geometry
2023-04-04 v1 Numerical Analysis
Mathematical Physics
Dynamical Systems
math.MP
Numerical Analysis
Symplectic Geometry
Abstract
We use local symplectic Lie groupoids to construct Poisson integrators for generic Poisson structures. More precisely, recursively obtained solutions of a Hamilton-Jacobi-like equation are interpreted as Lagrangian bisections in a neighborhood of the unit manifold, that, in turn, give Poisson integrators. We also insist on the role of the Magnus formula, in the context of Poisson geometry, for the backward analysis of such integrators.
Cite
@article{arxiv.2205.04838,
title = {Symplectic Groupoids for Poisson Integrators},
author = {Oscar Cosserat},
journal= {arXiv preprint arXiv:2205.04838},
year = {2023}
}