Multidimensional singular lambda-lemma

The well known $lambda$-Lemma [3] states the following: Let $f$ be a $C^1$-diffeomorphism of $mathbb{R}^n$ with a hyperbolic fixed point at $0$ and $m$- and $p$-dimensional stable and unstable manifolds $W^S$ and $W^U$, respectively ($m+p=n$). Let $D$ be a $p$-disk in $W^U$ and $w$ be another $p$-disk in $W^U$ meeting $W^S$ at some point $A$ transversely. Then $igcup_{ngeq 0} f^n(w)$ contains $p$-disks arbitrarily $C^1$-close to $D$. In this paper we will show that the same assertion still holds outside of an arbitrarily small neighborhood of $0$, even in the case of non-transverse homoclinic intersections with finite order of contact, if we assume that $0$ is a low order non-resonant point.