A theory of local convexity for a second order differential equation (${\text{sode}}$) on a Lie algebroid is developed. The particular case when the ${\text{sode}}$ is homogeneous quadratic is extensively discussed.

中文翻译：

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李代数上二阶微分方程的局部凸性

建立了李代数上二阶微分方程 (${\text{sode}}$) 的局部凸性理论。广泛讨论了 ${\text{sode}}$ 是齐次二次方的特殊情况。