The purpose of this paper is to show that the lattice Sn of permutations on a n-element set is bounded. This result strengthens the semi-distributive nature of the lattice Sn. To prove this property, we use a characterization of the class of bounded lattices in terms of arrows relations defined...

We investigate the stability problem for a nonlinear autoregressive model with Markov switching. First we give conditions for the existence and the uniqueness of a stationary ergodic solution. The existence of moments of such a solution is then examined and we establish a strong law numbers for...

For a given finite poset (P,-<), we construct strict completions of P which are models of all finite lattices L such that the set of join-irreducible elements of L is isomorphic to P.

In this paper, we study almost periodic (a.p.) solutions of discrete dynamical systems. We first adapt some results on a.p. differential equations to a.p. difference equations, on the link between boundedness of solutions and existence of a.p. solutions.

We are interested by Lyapounov exponents in the almost periodic Hamiltonian case.

We have recalled that all interval doubling schemes of a bounded lattice L are in bijection with all different ways to conduct L starting from the two-element lattice by doublings of convex sets.