# locally maximal

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

 $\Lambda=\bigcap_{n=-\infty}^{\infty}f^{n}(\overline{U}).$
Title locally maximal LocallyMaximal 2013-03-22 14:07:24 2013-03-22 14:07:24 Koro (127) Koro (127) 5 Koro (127) Definition msc 37B35 msc 37D05 basic set