Abstract: A dynamical system based motion representation for obstacle avoidance and motion learning is proposed. The obstacle avoidance problem can be inverted to enforce that the flow remains enclosed within a given volume. A robot arm can be controlled by using the $\Gamma$-field in combination with the converging dynamical system. The closed-form model is extended to time-varying environments, i.e., moving, expanding and shrinking obstacles. This is applied to an autonomous robot (QOLO) in a dynamic crowd in the center of Lausanne. Using Gaussian Mixture Regression (GMR) motion can be learned by describing them as a combination of local rotations. The motion can be further refined to create a safe invariant set within the obstacles' hull.