Structurally Stable

A Map $\phi:M\to M$ where $M$ is a Manifold is $C^r$ structurally stable if any $C^r$ perturbation is Topologically Conjugate to $\phi$. Here, $C^r$ perturbation means a Function $\psi$ such that $\psi$ is close to $\phi$ and the first $r$ derivatives of $\psi$ are close to those of $\phi$.

See also Topologically Conjugate