Each of the obtained pull-back attractors is represented by a segment on the fiber (whose length might be zero). In this step, we use evolution towards the target fiber from sufficiently long ago.

In part (2), we choose multiple target fibers that can be reached by forward iteration from the fiber chosen in (1). For each target fiber, we locate the images of the segments obtained in (1) and then try to decompose them to obtain the images of the repellers on the fiber. In the decomposition, we use forward iteration from the target fiber.

In part (3), we choose the zero-length segments obtained in (1) that represent pull-back attractors with negative lyapunov exponent, and calculate forward trajectory from each of the segments using segment map with small perturbation to $w$ component. We also calculate the forward iteration stating from segments that correspond to the basin of repellers that possibly has contact with the attractor in question. If these trajectories coincide after sufficiently long transient steps, that indicates the existence of a fiber on which the distance between the attractor and the repeller is smaller than the amplitude of the perturbation, which could be regarded as a signature of the 