Stability analysis for the pseudo-Riemannian geodesic flows of step-two nilpotent Lie groups
Dynamical Systems
2026-02-23 v3
Abstract
The present paper deals with the stability analysis for the geodesic flow of a step-two nilpotent Lie group equipped with a left-invariant pseudo-Riemannian metric. The Lie-Poisson equation can be described in terms of the so-called -mapping, a linear operator associated to the step-two nilpotent Lie algebras equipped with the induced scalar product. The stability of equilibrium points for the Hamilton equation is determined in terms of their Williamson types.
Keywords
Cite
@article{arxiv.2506.01058,
title = {Stability analysis for the pseudo-Riemannian geodesic flows of step-two nilpotent Lie groups},
author = {Genki Ishikawa and Daisuke Tarama},
journal= {arXiv preprint arXiv:2506.01058},
year = {2026}
}