M$ via :

$$\label{eqn:leaf1} W_b^* = \mbox{Im}(\ph_b \times
\textrm{Id}) \circ \ga (\b_b^*)$$

Here and below, $*$ stands for $s, u$ or blank space.\
Intuitively, $W_b^s$ denotes a center-stable leaf, $W_b^u$ denotes a central-unstable leaf, while $W_b$ denotes a central leaf. We will never consider strongly stable or unstable leaves.\
We now define certain functional spaces $\B^*$ of maps $\b^*$. These are, by definition, the spaces of Lipschitz maps that satisfy the condition:

$$\label{eqn:max} \max \left\{   \| \b^* \|_{C^0}, \frac {\mLip \b^*}D \right\}
\le \frac {\delta}2$$

Here, $D$ is a constant that will be picked in the proof of Lemma \[lem:1\]. The norm on the spaces $\B^*$ will always be the $C^0$ norm, and will be denoted by $||\cdot||$.\
Intuitively speaking, a central-stable, central-unstable or central *lamination* is a continuous assignment of leaves as $b$ runs over $\Lambda$. Rigorously speaking, a lamination is a continuous map:

$$\label{eqn:section} S^*:\Lambda \rightarrow \BB^*.$$

The map $S^*$ is completely determined by the continuous collection of maps $\b^*_b=S^*(b)$, as $b$ ranges over $\Lambda$. Equivalently, $S^*$ is completely determined by the leaves $W^*_b$ of these maps.\
The space of continuous sections $S^*$ as above is denoted by $\Ga^*$. The norm in this space is again the $C^0$ 