Electron. J. Diff. Eqns.,
Vol. 2003(2003), No. 38, pp. 1-9.
### Multidimensional singular
-lemma

Victoria Rayskin

**Abstract:**

The well known
-lemma
[3] states the following:
Let
be a
-diffeomorphism of
with a
hyperbolic fixed point at 0 and
- and
-dimensional stable
and unstable manifolds
and
, respectively
().
Let
be a
-disk
in
and
be another
p-disk
in
meeting
at some point
transversely. Then
contains
-disk arbitrarily
-close to
.
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.
Submitted November 4, 2002. Published April 11, 2003.

Math Subject Classifications: 37B10, 37C05, 37C15, 37D10.

Key Words: Homoclinic tangency, invariant manifolds, lambda-Lemma,
order of contact, resonance

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Victoria Rayskin

Department of Mathematics

MS Bldg, 6363

University of California at Los Angeles, 155505

Los Angeles, CA 90095, USA

email: vrayskin@math.ucla.edu

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