of those systems rather limited. In this paper we propose a method to identify and to locate repellers in quasi-periodically forced logistic map system, and exhibit the obtained images of repellers and bifurcation diagrams. It would be helpful for developing better understanding of mechanisms for the emergence of complex behaviors in quasi-periodically forced systems from dynamical system point of view.

introduction
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Quasi-periodically forced systems could be considered as one of the simplest class of “essentially non-autonomous” dynamical systems. In this class of systems, surprisingly complex dynamical phenomena, including rather common existence of strange non-chaotic attractors(SNA), were reported in early 1980s [@Grebogi-etal-84; @Kaneko-84a; @Kaneko-84b]. Since then the feature and the mechanism of such phenomena have been extensively studied by many researchers with various background, and related phenomena have been uncovered in relatively wide variety of systems [@Feudel-etal-06; @Ding-etal-89; @Prasad-etal-98; @Prasad-etal-07; @Senthilkumar-etal-08; @Mitsui-etal-12; @Suresh-etal-13]. Major part of the theoretical researches on the phenomena have been done mainly for the cases with systems with “forced” invariant set induced by something like symmetry [@Keller-96; @Yalcinkaya-Lai-97; @Yang-01; @Glendinning-02a; @Glendinning-02b; @Alseda-Misiurewics-08; @Bjerklov-12; @Bjerklov-09]. On the other hand, also for the systems without such forced invariant sets, rigorous results are obtained however mainly in reversible 1+1-dimensional 