Computation of the dominant Lyapunov exponent via spatial integration using matrix norms
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Aston, Philip J. and Dellnitz, M. (2003) Computation of the dominant Lyapunov exponent via spatial integration using matrix norms Proceedings of the Royal Society of London A, 459 . pp. 2933-2955.
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Abstract
In a previous paper (Aston, P. J. & Dellnitz, M. 1999 Comput. Meth. Appl. Mech. Engng 170, 223-237) we introduced a new method for computing the dominant Lyapunov exponent of a chaotic map by using spatial integration involving a matrix norm. We conjectured that this sequence of integrals decayed proportional to 1/n. We now prove this conjecture and derive a bound on the next term in the asymptotic expansion of the terms in the sequence. The Hénon map and a system of coupled Duffing oscillators are explored in detail in the light of these theoretical results.
| Item Type: | Article |
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| Additional Information: | Published in Proceedings of the Royal Society of London A, 459, 2933-2955. © 2003 The Royal Society. All rights reserved. |
| Uncontrolled Keywords: | Lyapunov Exponents, Invariant Measure, Subdivision Algorithm, Blowout Bifurcation |
| Divisions: | Faculty of Engineering and Physical Sciences > Mathematics |
| ID Code: | 1551 |
| Deposited By: | Mr Adam Field |
| Deposited On: | 27 May 2010 15:42 |
| Last Modified: | 28 Sep 2012 10:50 |
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