PlanetMath: locally maximal

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locally maximal

(Definition)

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

$\displaystyle \Lambda=\bigcap_{n=-\infty}^\infty f^n(\overline{U}).$

"locally maximal" is owned by Koro.

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Other names:

basic set

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Cross-references: neighborhood, hyperbolic set, smooth manifold, diffeomorphism
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This is version 2 of locally maximal, born on 2004-01-20, modified 2004-01-20.
Object id is 5530, canonical name is LocallyMaximal.
Accessed 5391 times total.

Classification:

AMS MSC:	37B35 (Dynamical systems and ergodic theory :: Topological dynamics :: Gradient-like and recurrent behavior; isolated invariant sets)
	37D05 (Dynamical systems and ergodic theory :: Dynamical systems with hyperbolic behavior :: Hyperbolic orbits and sets)

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