Hello,
I am afraid my quest is desperate ... but... I would like to estimate numerically this metric on a chaotic attractor so as to compute the unstable divergence of a vector field (the projected divergence along the unstable manifold). I am looking for any hints on the question.
Many thanks
Bruno
Isn't the lyapunov exponent computed along a trajectory ? Would u have to compute the lyapunov exponent along geodesic flows on a surface ?
Also, is it possible that there is a vector of lyapunov exponents, one for each eigen-curve / basis curve of the surface / manifold ?
Dear Sundaram
Thanks for your reply. Yes, you are right, the computation would start by computing the Lyapunov spectrum (not only the largest Lyapunov exponents, because several exponents can be positive). But I need then the corresponding unstable directions, which can be computed using QR decomposition and Eckmann-Ruelle algorithm. Then I would have to compute the derivative of the vector field projected on these directions. This could be a bit hard numerically because it requires many points, and I want to compute this derivative along the attractor. I don't know if there are any example of analytical results that would be helpful to check the reliability of the algorithm.
Many thanks,
Bruno
- Badges
- Science topic
- Similar topics
- Correction