Topological properties of asymptotically stable sets

Emmanuel Moulay (1) , Sanjay P. Bhat (2)

1 SIC
2 TCS Innovation Labs [Hyderabad]

Topological properties of the domain of attraction for dynamical systems are investigated. The main purpose of this paper is to prove that a compact, asymptotically stable attractor of a dynamical system defined on a locally compact metric space is a deformation retract of its domain of attraction, in a weak sense that is made precise. Under additional local assumptions, the attractor can be shown to be a retract, a deformation retract, or a strong deformation retract. The well known result that the domain of attraction of an asymptotically stable equilibrium is contractible follows as a corollary.

Mots clés: Asymptotically stable sets; domain of attraction; retraction; Lyapunov functions

Domaines: Optimisation et contrôle [math.OC]

Emmanuel Moulay, Sanjay P. Bhat. Topological properties of asymptotically stable sets. Nonlinear Analysis: Theory, Methods and Applications, 2010, 73 (4), pp.1093-1097. ⟨10.1016/j.na.2010.04.043⟩. ⟨hal-00551285⟩