# 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.

Title attracting fixed point AttractingFixedPoint 2013-03-22 13:06:24 2013-03-22 13:06:24 PrimeFan (13766) PrimeFan (13766) 6 PrimeFan (13766) Definition msc 37C75 GloballyAttractingFixedPoint LiapunovStable StableFixedPoint NeutrallyStableFixedPoint UnstableFixedPoint