🚀 go-pugleaf

In <2poha4$fqa@portal.gmu.edu> [sci.nonlinear], HARRY R. ERWIN (herwin@mason1.gmu.edu) wrote:
>I'm currently working through Abarbanel, et al., "The Analysis of
>Observed Chaotic Data in Physical Systems," but that turns out to apply
>to conservative systems with constant Kolmogorov-Sinai entropy, and my
did you carefully read that paper ?
You should have a second reading: most of the material contained in that paper
deals with dissipative systems, if not all.
what does "constant Kolmogorov-Sinai" mean ?
constant with respect to parameters ? yes if you have a structurally stable
invariant set, however these are generally not attractors and not the kind
of things Abarbanel et al. consider in their paper (they are interested
in the analysis of physical data).
With respect to time ? does not make sense, since KS entropy is an average
with respect to the natural measure.   
>interest is in dissipative systems, with changing dimension and
changing dimension with respect to what ?
>transients. Back in 1990, I was already wrestling with this, and in my
>paper for the Cambridge Conference, I proposed to use topological

interesting, which properties ?

>properties to characterize these systems. For example, one of the key
>concerns of peer polity elites was maintaining constant dimension, since
                                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
again what does that mean ? dimension can only be changed by varying 
control parameters. I know of no way to maintain a constant dimension
when changing parameters unless you have a periodic regime

>the most disruptive perturbations were those that created transient 
>increases in the dimension of the system, so that it became chaotically 
>uncontrollable. There are similar issues in neurodynamics.

>Does anyone have any references to papers addressing the analysis of
>data from systems with dissipative chaos?

The one you quote in the beggining of your post
>--
>Harry Erwin
>Internet: herwin@gmu.edu 
>Working on Katchalsky nets....

--
________________________________________________________________________
| Marc Lefranc, Laboratoire de Spectroscopie Hertzienne (URA CNRS 249) |
| Bat P5, UFR de Physique                                              |
| Universite des Sciences et Technologies de Lille                     |
| F-59655 Villeneuve d'Ascq CEDEX (FRANCE)                             |
| e-mail: lefranc@lsh.univ-lille1.fr                                   |
|______________________________________________________________________|