Definition:Directed Smooth Curve/Parameterization/Complex Plane/Reparameterization
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Definition
Let $\gamma : \closedint a b \to \C$ be a smooth path in $\C$.
Let $C$ be a directed smooth curve in the complex plane $\C$ parameterized by $\gamma$.
Let $\phi: \closedint c d \to \closedint a b$ be a bijective differentiable strictly increasing real function.
Let $\sigma : \closedint c d \to \C$ be defined by:
- $\sigma = \gamma \circ \phi$
Then $\sigma$ is called a reparameterization of $C$.
Sources
- 2001: Christian Berg: Kompleks funktionsteori $\S 2.2$