🚀 go-pugleaf

Jim Heagy (jheagy@zoltar.nrl.navy.mil) wrote:
: In article <2poha4$fqa@portal.gmu.edu>, herwin@mason1.gmu.edu (HARRY R.
: ERWIN) wrote:

: > Does anyone have any references to papers addressing the analysis of
: > data from systems with dissipative chaos?
: > 
: There is a method of topolocial data analysis that concerns the
: connectivity and intertwining properties of unstable periodid orbits in a
: chaotic attractor. As far as I know, this is the only method of chaotic
: data analysis that can be used to definitively REJECT proposed models for
: the data.  See the references

: G. B. Mindlin, H. G. Solari, et al, "Topological Analysis of Chaotic Time
: Series ...", J. Nonlin. Sci. 2, 147 (1991).

: G. B. Mindlin, X.-J. Hou, et al, "Classification of Strange Attractors by
: Integers", Phys. Rev. Lett. 64, 2350 (1990).

: N. B. Tufillaro, H. G. Solari and R. Gilmore, "Relative Rotation Rates:
: Fingerprints for Strange Attractors", Phys. Rev. A 41, 5717, (1990).

Does any of this work for dimensions > 3 ?  

I thought heard/read that all knots untie in 4 dimensions, preventing
this interesting topological analysis from working.

If there were some way to make this work in arbitrary dimensions, it could
be quite powerful.

cheers
Matt

--
-Matt Kennel  		mbk@inls1.ucsd.edu
-Institute for Nonlinear Science, University of California, San Diego
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