I would like to read more about invariant manifolds or slow manifolds. Does anyone know good reviews on these? In particular, I have read Lorenz's paper on slow manifolds that are not invariant, and wonder whether there has been further work developing this idea.
Thanks! Some of these I did not find myself. Roberts89b looks interesting to me. I will read it to see whether he talks about slow but not invariant manifolds.
The paper that I referred to is E. N. Lorenz, “The slow manifold — what is it?”, Journal of the Atmospheric Sciences, vol. 49, pp. 2449–2451, 1992.
Someone pointed me to another very interesting review on the separation into slow and fast variables.
Sergio Rinaldi and Marten Scheffer, 2000. Geometric Analysis of Ecological
Models with Slow and Fast Processes. Ecosystems, vol. 3, pp. 507-521.
Concerning the paper of Eward Norton Lorenz you can directly download it on the web: http://eaps4.mit.edu/research/Lorenz/Slow_man_what_92.pdf. Concerning the slow manifold determination you can see the new approach that I have developed and called Flow Curvature Method: http://ginoux.univ-tln.fr
Dear Marc, first I have to say that the Flow Curvature Method has been elaborated three years before IDLM, in 2005 during my Ph-D thesis and secondly this method is slightly different since it is based on the concept of curvature which is inherent to Differential Geometry. I can send you significant papers exemplifying the efficiency and the simplicity of my method.
Hi i'm working on regulation output problem and I would like that you help me with some references about the stability of an infinite dimensional nonautonomous linear system. Especially defining the spectrall bound of the matrix operator of the augmented system. Thank you.
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