Talk:Lyapunov exponent
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[edit] Numerical computation
I removed the citation:
- Sprott J. C. Chaos and Time-Series Analysis Oxford University Press, 2003—see also online supplement Numerical Calculation of Largest Lyapunov Exponent
because the method described in that online supplement should be limited to the case when the equation of motion is not known analytically. When the equations of motion are known, the method described in the Wikipedia article can be implemented directly. It provides the entire spectrum and better analytic control.
The computation of the Lyapunov exponents is not without its perils. As an experiment, try computing the Lyapunov exponents for the canonical Hénon map and for the Hénon map with a = 1.39945219 and b = 0.3. XaosBits 04:43, 9 January 2006 (UTC)
[edit] Incorrect Formula for Maximal Lyapunov Exponent
It should only be the limit of t to infinity, not also the limit of delta zero to infinity as the limit of delta zero to infinity alone is the definition for the short-time Lyapunov exponent according to Siopis, Christos, Barbara L. Eckstein, and Henry E. Kandrup. “Orbital Complexity, Short-Time Lyapunov Exponents, and Phase Space Transport in Time-Independent Hamiltonian Systems.” Annals of the New York Academy of Sciences, Vol. 867. (Dec. 30, 1998), pp. 41-60.--Waxsin 22:36, 2 October 2007 (UTC)
Strogatz, Steven H "Nonlinear Dynamics and Chaos" (Ch. 10.5) defines the maximal Lyapunov exponent with the just the limit of t to infinity, as does many others.--Waxsin 22:36, 2 October 2007 (UTC)
[edit] A bit too abstract
The article is helpful for those who already have a grasp on multidimensional dynamical systems. As a layman and non-mathematician however, I'd prefer if a special, less abstract explanation was provided. I found several explanations for the Lyapunov exponent in simple one dimensional systems on the web. It should be easy for someone with a background in mathematics to add such an alternative perspective for the uninitiated to the article. Thank you! --89.48.244.241 12:26, 5 September 2006 (UTC)
[edit] Positive Lyapunov exponent
It's easy to have non-chaotic system with positive lyapunov exponent, for instance x_{i+1}=2x_i
