Area-Preserving Map

A Map $F$ from $\Bbb{R}^n$ to $\Bbb{R}^n$ is Area-preserving if

$$m(F(A)) = m(A)$$

for every subregion $A$ of $\Bbb{R}^n$, where $m(A)$ is the $n$-D Measure of $A$. A linear transformation is Area-preserving if its corresponding Determinant is equal to 1.

See also Conformal Map, Symplectic Map