The Carathéodory-Rashevsky-Chow theorem for the nonholonomic Lipschitz distributions (Q2436107)

In the paper under review, the author deals with certain problems concerning \(k\)--dimensional Lipschitz distributions in \({\mathbb R}^{k+1}\). The main results of the paper are listed below. {Theorem 1}. Let \(H\) be a \(k\)--dimensional nonholonomic Lipschitz distribution in a connected domain \(U \subset {\mathbb R}^{k+1}\). Then every two points \(p\), \(q \in U\) are \(H\)-connectable. {Theorem 2}. Let \(H\) be a nice \(k\)-dimensional distribution in \({\mathbb R}^{k+1}\) generated by continuous vector fields \(X_1,X_2,\dots,X_k\). If \(H\) is nonholonomic in a connected domain \(U\), then every pair of points \(p\), \(q \in U\) is \(H\)-connectable.