at times $n=1,2,..,m$. One of the simplest ansatz would be to write down a piecewise linear expression for $h_f$. Our knowledge of the properties and dynamics of $1-d$ maps however suggests that the local behaviour of the map in the neighbourhood of special points, like for example a marginal unstable fixed point in the case of intermittent dynamics (see ref.[@Ott] and references therein), plays a crucial role in determining the statistical properties of the map. A more intuitive ansatz is therefore needed. Here we will proceed as follows.\
We define a $1-d$ lattice with $N+1$ points in the interval $[0,x_{\max}]$. The coordinates of the lattice points are $x_p(i),~i=0,1,..,N$ with $x_p(0)=0$ and $x_p(N)=x_{\max}$. The function $h_f(x)$ is piecewice defined. We will call in the following the expression of $h_f$ in the $i-th$ interval $[x_p(i-1),x_p(i))$ an [**[element]{}**]{} and use the notation $h_{f,i}$ for the $i-th$ element. In practice one is free to choose many different expressions for the $i$-th element. Constraints on $h_f$ as for example continuity in $[0,x_{\max}]$ together with the conditions (\[hfprei\],\[hfprop\]) however restrict the possible forms. A desirable but not necessary requirement is that $h_{f,i}$ should be analytically invertible in order to easily extend the solution in $[0,x_{\max}]$ to 