Abstract (EN)

We study recursive inclusionsx n+1 ε G(x n ). For instance, such systems appear for discrete finite-difference inclusionsx n+1 εG ρ (x n) whereG ρ :=1+ρF. The discrete viability kernel ofG ρ , i.e., the largest discrete viability domain, can be an internal approximation of the viability kernel ofK underF. We study discrete and finite dynamical systems. In the Lipschitz case we get a generalization to differential inclusions of the Euler and Runge-Kutta methods. We prove first that the viability kernel ofK underF can be approached by a sequence of discrete viability kernels associated withx n+1 εГ ρ (xn) whereГ ρ (x) =x + ρF(x) + (ML/2) ρ 2ℬ. Secondly, we show that it can be approached by finite viability kernels associated withx h n+1 ε (Г ρ (x h n+1 ) +α(hℬ) ∩X h .