attracting fixed point

Let X be a vector field on a manifold M and let Ft be the flow of X. A fixed pointMathworldPlanetmath x* of X is called attracting if there exists a neighborhoodMathworldPlanetmathPlanetmath U of x* such that for every xU, Ft(x)x* as t.

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