The shaded region in the picture is bounded by the stable and
unstable manifold segments of the fixed points and contains the
invariant set. Let denote a
boundary point that is not on the stable manifold of any of the fixed points.
D
(
) is a small disk of radius
centered at
,
and L
(
) is a horizontal line segment through
contained in D
(
). For a sufficient number of iterates m,
fm(L
(
)) will cross segments of the stable manifold bounding
the shaded region.