How chaotic are strange nonchaotic attractors?

Glendinning, Paul and Jager, Tobias and Keller, Gerhard (2006) How chaotic are strange nonchaotic attractors? [MIMS Preprint]

PDF gjksdic-final.pdf Download (317kB)

Abstract

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 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 39 Difference and functional equations
Depositing User:	Professor Paul Glendinning
Date Deposited:	17 May 2006
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/235

Actions (login required)

View Item