We present an example of slow-fast system which
displays a full open set of initial data so that the corresponding
orbit has the property that given any $\epsilon$ and $T$, it
remains to a distance less than $\epsilon$ from a repulsive part
of the fast dynamics and for a time larger than $T$. This example
shows that the common representation of generic fast-slow systems
where general orbits are pieces of slow motions near the
attractive parts of the critical manifold intertwined by fast
motions is false. Such a description is indeed based on the
condition that the singularities of the critical set are folds. In our
example, these singularities are transcritical.