No abstract

No abstract

We study recursive inclusions x n+1 ∈ G(x n). For instance such systems appear for discrete finite difference inclusions x n+1 ∈ Gρ(x n) where Gρ := 1 + ρF. The discrete viability kernel of Gρ, i.e. the largest discrete viability domain, can be an internal approximation of the viability kernel of K under F. We study discrete and finite dynamical systems. In the Lipschitz case we get a generalization to differential inclusions of Euler and Runge-Kutta methods. We prove first that the viability kernel of K under F can be approached by a sequence of discrete viability kernels :associated with Γρ(x) = x + ρF (x) + M l 2 ρ 2 B. Secondly, we show that it can be approached by finite viability kernels associated with Γ α hρ (x) := x + ρF (x) : x n+1 h ∈ (Γ hρ (x n h) + α(h)B) ∩ X h .