other attractors. \[FIG:DIAGRAM\]

The obtained phase diagram (Fig.\[FIG:DIAGRAM\]) seems similar to those obtained in the preceding studies. However, since our criterion to identify an attractor as SNA is different from those used in the preceding studies (based on the divergence of the estimated phase sensitivity), the position of the obtained borderline between smooth attracting torus and SNA has some discrepancy. It would be notable that we observed no SNA near the border of the boundary crisis which is associated with the disappearance of bounded attractor in the bump-like region near $(a,e)=(1.2, 0.42)$ (as is shown in box (c)), which is consistent with the natural expectation that SNA appears only AT the boundary crisis for such cases.

An example of the repellers with non-trivial structure (observed as “ring shaped” repellers in RA method) is exhibited in Fig. \[FIG:typical-example\]. Besides the apparently fractal layered structure, thin apertures can be observed in the rim of the rings (in boxes b and c). These thin apertures are mapped to the large gap near $\theta=0.35$ (indicated by a two-way arrow in box a), after 15 (for box b) and 28 (for box c) iterations.

The above result suggests that the repeller has a family of 