In this paper we will consider Foata map as a function which associates another permutation, known as F(δ), to each permutation δ = δ 1 δ 2 ⋅ ⋅ ⋅ δ m of the integers {1, 2, . . . ,m}, in such a way that the number of cycles of δ is equal to the number of left to right minima of F(δ). We will analyze the behaviour of the iterated maps, F2(δ) = Fδ(F(δ)), F3(δ), ... and so on. It is clear that given a permutation δ, positive integer numbers k exist such that Fk(δ) = . Consider the smallest of these numbers and call it n. We shall call the (ordered) set of permutations C(δ) = {δ, F(δ), . . . , Fn−1(δ)} a Foata circuit and n its length. The length of Foata circuits is the main concern of this paper: to our knowledge, no study has been devoted to this subject yet. Experimental results are quite surprising. In computable cases, generally speaking, there are one (at most two) circuit(s) of very large length (up to 85% of the total number of permutations) and a number of little circuits, even of some units of components. In this paper we will give a list of these circuits for permutations up to 11 elements. However these data give rise to some conjectures, difficult to verify: the investigation on permutations of more than 10 elements is a challenge and the case of m = 11 is a demonstration of this issue! At the same time, in this paper we will also discuss some properties of 'short' circuits, i.e. the ones consisting in 2, 3 or 4 permutations.