Straightening theorem for vector fields

In differential calculus, the domain-straightening theorem states that, given a vector field X {\displaystyle X} on a manifold, there exist local coordinates y 1 , … , y n {\displaystyle y_{1},\dots ,y_{n}} such that X = ∂ / ∂ y 1 {\displaystyle X=\partial /\partial y_{1}} in a neighborhood of a point where X {\displaystyle X} is nonzero. The theorem is also known as straightening out of a vector field.

Source: Wikipedia — Straightening theorem for vector fields (CC BY-SA 4.0)