How chaotic are strange nonchaotic attractors

Details How chaotic are strange nonchaotic attractors How chaotic are strange nonchaotic attractors

2006-04-13

arxiv.org/abs/math/0604309v1

Mathematics

Dynamical Systems

19 pages, 2 figures

Scientific paper

10.1088/0951-7715/19/9/001

We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general classes of quasiperiodically forced systems. Further, we include an elementary proof of a classic result by Glasner and Weiss on sensitive dependence, and we clarify the structure of the attractor in an example with two-dimensional fibers also introduced by Grebogi et al.

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