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

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

Title	locally maximal
Canonical name	LocallyMaximal
Date of creation	2013-03-22 14:07:24
Last modified on	2013-03-22 14:07:24
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	5
Author	Koro (127)
Entry type	Definition
Classification	msc 37B35
Classification	msc 37D05
Synonym	basic set