# Stability of geodesic vectors in low-dimensional Lie algebras

@inproceedings{Nguyen2022StabilityOG, title={Stability of geodesic vectors in low-dimensional Lie algebras}, author={Annie Nguyen and Yuri Nikolayevsky}, year={2022} }

A naturally parameterised curve in a Lie group with a left invariant metric is a geodesic, if its tangent vector left-translated to the identity satisfies the Euler equation Ẏ = ad Y Y on the Lie algebra g of G. Stationary points (equilibria) of the Euler equation are called geodesic vectors: the geodesic starting at the identity in the direction of a geodesic vector is a one-parameter subgroup of G. We give a complete classification of Lyapunov stable and unstable geodesic vectors for metric…

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