Stability analysis for the pseudo-Riemannian geodesic flows of step-two nilpotent Lie groups

2025/06/01 by Ishikawa, Genki, Tarama, Daisuke
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2506.01058

openalex publication_date 2025/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 j-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.

Citations

• Real non-degenerate two-step nilpotent Lie algebras of dimension eight
• On first integrals of the geodesic flow on Heisenberg nilmanifolds
• Singularities of integrable systems and algebraic curves
• Pseudo-metric 2-step nilpotent Lie algebras
• Stability of relative equilibria of multidimensional rigid body
• 2-step nilpotent Lie groups arising from semisimple modules
• Integrable geodesic flows with wild first integrals: the case of two-step nilmanifolds
• Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities

Related

• Stability of geodesic vectors in low-dimensional Lie algebras
• Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules
• Pseudoriemannian 2-Step Nilpotent Lie Groups
• Linear flows on compact, semisimple Lie groups: stability, periodic orbits, and Poincaré-Bendixon's Theorem
• Positive Hermitian curvature flow on complex 2-step nilpotent Lie groups