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

Genki Ishikawa; Daisuke Tarama

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arXiv · 2506.01058

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

Genki Ishikawa·Daisuke Tarama

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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.

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BibTeX RIS

Genki Ishikawa, Daisuke Tarama. 2025-06-01. Stability analysis for the pseudo-Riemannian geodesic flows of step-two nilpotent Lie groups. https://arxiv.org/abs/2506.01058

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