locally maximal

Let $f:M\to M$ be a diffeomorphism of a smooth manifold $M$, and let $\mathrm{\Lambda }$ be a hyperbolic set for $f$. We say that $\mathrm{\Lambda }$ is locally maximal or basic if there exists a neighborhood $U$ of $\mathrm{\Lambda }$ such that

$$\mathrm{\Lambda }=\bigcap _{n=-\mathrm{\infty }}^{\mathrm{\infty }}{f}^n(\overline{U}).$$