Whether strange nonchaotic attractors (SNAs) can typically arise in non-skew-product maps has been a crucial question for more than two decades. Recently, it was shown that SNAs arise in a particular non-skew-product map related to quasiperiodically driven continuous dynamical systems. In the present paper, we derive Badard's non-skew-product map from a periodically driven continuous dynamical system with spatially quasiperiodic potential and investigate onset mechanisms of SNAs in the map. In particular, we focus on a transition route to intermittent SNAs, where SNAs appear after pair annihilations of stable and unstable fixed points located on a ring-shaped invariant curve. Then the mean residence time and rotation numbers have a logarithmic singularity. Finally, we discuss the existence of SNAs in a special class of non-skew-product maps.
|ジャーナル||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|出版ステータス||Published - 2010 4 21|
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