  We propose a method to identify and to locate "repellers'' in
quasi-periodically forced logistic map (QPLM), using a kind of Morse
decomposition of nested attracting invariant sets. In order to obtain the
invariant sets, we use an auxiliary 1+2-dimensional skew-product map system
describing the evolution of a line segment in the phase space of QPLM. With
this method, detailed structure of repellers can be visualized, and the
emergence of a repeller in QPLM can be detected as an easily observable
bifurcation in the auxiliary system. In addition to the method to detect the
repellers, we propose a new numerical method for distinguishing a strange
non-chaotic attractor (SNA) from a smooth torus attractor, using a
correspondence between SNAs in QPLM and attractors with riddled basin in the
auxiliary system.
