Reparametrization

Definition

Let $\gamma :[a,b]\to \mathbb{C}$ be a Smooth Parametrization of a curve $C$.

We say that $\sigma :[c,d]\to \mathbb{C}$ is a reparametrization of $\gamma$ if there exists a function $\alpha :[c,d]\to [a,b]$ such that $\sigma (t)=\gamma (\alpha (t))$ for all $t\in [c,d]$.