Computation of the dominant Lyapunov exponent via spatial integration using matrix norms
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.
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.
|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|
|Depositing User:||Mr Adam Field|
|Date Deposited:||27 May 2010 14:42|
|Last Modified:||23 Sep 2013 18:33|
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