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 ?

diffeomorphism, right? – drbobmeister Jan 11 '11 at 2:56