Computation of the dominant Lyapunov exponent via spatial integration using matrix norms | Zendy

Philip J. Aston | Zendy; Michael Dellnitz | Zendy

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Computation of the dominant Lyapunov exponent via spatial integration using matrix norms

Author(s) -

Philip J. Aston,

Michael Dellnitz

Publication year - 2003

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2003.1143

Subject(s) - lyapunov exponent , chaotic , mathematics , computation , conjecture , sequence (biology) , exponent , matrix (chemical analysis) , norm (philosophy) , duffing equation , pure mathematics , mathematical analysis , computer science , physics , algorithm , linguistics , philosophy , materials science , nonlinear system , quantum mechanics , artificial intelligence , biology , political science , law , composite material , genetics

In a previous paper (Comput. Methods Appl. Mech. Engrg 170, 223-237, 1999) 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 H´enon map and a system of coupled Dung,oscillators are explored in detail in the light of these theoretical results.

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