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# attracting fixed point

Let $X$ be a vector field on a manifold $M$ and let $F_{t}$ be the flow of $X$. A fixed point $x^{*}$ of $X$ is called attracting if there exists a neighborhood $U$ of $x^{*}$ such that for every $x\in U$, $F_{{t}}(x)\to x^{*}$ as $t\to\infty$.

The stability of a fixed point can also be classified as stable, unstable, neutrally stable, and Liapunov stable.

Related:

GloballyAttractingFixedPoint, LiapunovStable, StableFixedPoint, NeutrallyStableFixedPoint, UnstableFixedPoint

Type of Math Object:

Definition

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Reference

## Mathematics Subject Classification

37C75*no label found*

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## Comments

## lease merge this article with the planet math article "perio...

Please merge this article with the planet math article "periodic point"

## Re: lease merge this article with the planet math article "p...

How do I do that?