We describe classes of coordinate systems in Carnot-Carath\'eodory spaces of low smoothness which allow for homogeneous approximations of quasimetrics and basis vector fields. We establish the minimal smoothness required for these classes to coinside with the class of the privileged coordinates described earlier for the smooth case. We also apply these results to prove partial analogues of existing results in the canonical coordinates of the 2nd kind. As a geometric tool we prove some convergence theorems in quasimetric spaces.

中文翻译：

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较低平滑度的 Carnot-Carathéodory 空间的特权坐标

我们描述了低平滑度的 Carnot-Carath\'eodory 空间中的坐标系类别，这些空间允许准度量和基向量场的齐次近似。我们建立了这些类所需的最小平滑度，以便与前面针对平滑情况描述的特权坐标类共存。我们还应用这些结果来证明第二类规范坐标中现有结果的部分类似物。作为几何工具，我们证明了拟度量空间中的一些收敛定理。