Stability analysis for the pseudo-Riemannian geodesic flows of step-two nilpotent Lie groups
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 is formulated using the so-called [Formula: see text]-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.
Fields of Study & Subjects
Advanced Differential Geometry Research
Control and Stability of Dynamical Systems
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Geometric Mechanics
- Volume
- 03
- Issue
- 01
- Pages
- 1–34
- Publication date
- 12 February 2026
- Language
- EN