Work

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

Year: 2026

Type: article

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.

Source: Geometric Mechanics

DOI: 10.1142/s2972458926500012

Authors: Genki Ishikawa, Daisuke Tarama

Institution: Ritsumeikan University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Japan Society for the Promotion of Science, Japan Science and Technology Agency

Awards: Dynamical Systems and Geometric Structures: Symmetry, Singularity, and Quantization, G2943184455, Development of innovative theories on integrability of dynamical systems and their applications, G4924060474, G5347945865