CONLUSION

We learn by this quick look to a dicret system that for some value of parameters a, b, l and r the system converge to the attractor called Ikeda. This attractror still not well-known, nevertheless a theoritical study gives way to a determent of Jacobian matrix equal to b², it means that an area in the basin of attraction is contracted after each iteration by a factor of b²; then after n iterations we have a contraction of b^2n. When n tend to infinit the area tend to zero, it is strange but logical because the attractor's area is null.