Coordinates Adapted to Vector Fields: Canonical Coordinates

@article{Stovall2017CoordinatesAT,
  title={Coordinates Adapted to Vector Fields: Canonical Coordinates},
  author={Betsy Stovall and Brian Street},
  journal={Geometric and Functional Analysis},
  year={2017},
  volume={28},
  pages={1780-1862}
}
Given a finite collection of C1 vector fields on aC2 manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields have a higher level of smoothness. For example, when is there a coordinate system in which the vector fields are smooth, or real analytic, or have Zygmund regularity of some finite order? We address this question in a quantitative way, which strengthens and generalizes previous works on the… CONTINUE READING