Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
This lecture discusses the concept of local invertibility of vector fields, where a vector field is considered locally invertible at a point if it is invertible within a ball centered at that point. The instructor explains the conditions for a vector field to be locally invertible and the implications of its inverse being C¹. The lecture also covers the Inverse Function Theorem, stating that a vector field that is C¹ and has an invertible Jacobian matrix is locally invertible. Various examples are provided to illustrate the criteria for invertibility and non-invertibility of vector fields.