for starting point corresponding to sufficiently short segments is expected to be one of the attractors of the segment map. Let $A$ denote the attractor. The ensemble of orbits starting from a neighborhood of the original point $p$ should be dense in the shadow of the attractor $A$. Thus the shadow of the attractor $A$ could be regarded as a “basin of repulsion” of the repelling non-wandering point $p$.

There can be multiple repelling non-wandering points with the common “basin of repulsion”. The set of those repelling non-wandering points consist a transitive set. Thus the set as a whole could be identified as a “repeller”. We let $R(A)$ denotes a repeller with “basin of repulsion” $A$.

Basically what we try to obtain is a image of the section of repellers on a target fiber. In order to do this, we try to carry out the following steps.

-   Obtain the list of pull back attractors of the segment map on the target fiber,

-   Find pull back attractors that correspond to a segment whose proper subset corresponds to another pull back attractor,

-   Look for such points which are in the shadow of the outer attractor and whose corresponding $\omega$-limit 