2006.85: How chaotic are strange nonchaotic attractors?
2006.85: Paul Glendinning, Tobias Jager and Gerhard Keller (2006) How chaotic are strange nonchaotic attractors?
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We show that the classic examples of quasi-periodically 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 bers also introduced by Grebogi et al.
|Item Type:||MIMS Preprint|
|Subjects:||MSC 2000 > 37 Dynamical systems and ergodic theory|
MSC 2000 > 39 Difference and functional equations
|Deposited By:||Professor Paul Glendinning|
|Deposited On:||17 May 2006|