Let be $\Lambda$ a hosrseshoe for a $C^r$ ($r\geq2$) dipheomorphism $f:M\to M$ where $M$ is a two dimensional manifold. A well-known result is the following:


for each $x\in \Lambda$ let be $W^u(x)$ and $W^s(x)$ the unstable and stable manifolds respectively of $f$ in $x$. Then exists neighborhoods $\mathcal{V}\_1$ and $\cal{V}\_2$ of $\Lambda$ where are defined $C^1$ foliations $\cal{F}\_1$ and $\cal{F}\_2$ 
such that $T\_p\mathcal{F}\_1=E^u\_p$ and $T\_p\mathcal{F}\_2=E^s\_p$ where $T\_p\mathcal{F}\_i$ denotes
the tangent space on the leave $\cal{F}\_i$.


My question is: how construct this foliations ?



Local Product Struture
You can find an alternative proof (to the one of Palis Takens) in section 6.4 of [this survey](http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.2896v1.pdf).


