Category:Definitions/Directed Smooth Curves (Complex Plane)
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This category contains definitions related to Directed Smooth Curves (Complex Plane).
Related results can be found in Category:Directed Smooth Curves (Complex Plane).
Let $\gamma : \closedint a b \to \C$ be a smooth path in $\C$.
The directed smooth curve with parameterization $\gamma$ is defined as an equivalence class of smooth paths as follows:
A smooth path $\sigma: \closedint c d \to \C$ belongs to the equivalence class of $\gamma$ if and only if:
- there exists a bijective differentiable strictly increasing real function:
- $\phi: \closedint c d \to \closedint a b$
- such that $\sigma = \gamma \circ \phi$.
Pages in category "Definitions/Directed Smooth Curves (Complex Plane)"
The following 6 pages are in this category, out of 6 total.