Lyapunov stable

A fixed pointMathworldPlanetmath x* is Lyapunov stablePlanetmathPlanetmath if trajectories of nearby points x remain close for future time. More formally the fixed point x* is Lyapunov stable, if for any ϵ>0, there is a δ>0 such that for all t0 and for all xx* it is verified


In particular, d(x*,x(0))=0.

Title Lyapunov stable
Canonical name LyapunovStable
Date of creation 2013-03-22 13:06:29
Last modified on 2013-03-22 13:06:29
Owner armbrusterb (897)
Last modified by armbrusterb (897)
Numerical id 10
Author armbrusterb (897)
Entry type Definition
Classification msc 34D20
Synonym Lyapunov stability
Synonym Liapunov stable
Synonym Liapunov stability
Related topic AsymptoticallyStable
Related topic AttractingFixedPoint
Related topic StableFixedPoint
Related topic NeutrallyStableFixedPoint
Related topic UnstableFixedPoint