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 $t\to \mathrm{\infty }$.

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

Title	attracting fixed point
Canonical name	AttractingFixedPoint
Date of creation	2013-03-22 13:06:24
Last modified on	2013-03-22 13:06:24
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	6
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 37C75
Related topic	GloballyAttractingFixedPoint
Related topic	LiapunovStable
Related topic	StableFixedPoint
Related topic	NeutrallyStableFixedPoint
Related topic	UnstableFixedPoint