English

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 jj-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}
}