Les,
Guess you had better send me your email
address and we can deal with certain matters
offlist. Sorry figures not available on the website
version. They were supposed to be there.
I got the chaotic hysteresis thing from his
"cartoon" book with Shaw in 1987. The first
economic application was by Tonu Puu of Sweden
in a business cycle model in his 1989 _Nonlinear
Economic Dynamics_ (1st edn), Springer-Verlag,
but I only figured this out later.
I also cooked up the term "chaotic bubble"
(they are speculative bubbles that follow a chaotic
dynamic, duh), although the first application predated
the term, being in a very influential paper by my
editorial predecessor, Richard H. Day and his
student Weihong Huang, "Bulls, Bears, and Market
Sheep," JEBO, 1990, vol. 14, pp. 299-329. Real
world bubbles look more like this than the usual
sort of smoothly moving babies one sees in most
theoretical models.
Yeah, the stuff with Marsden, etc. tends to be
more soporific, definitely not acid-drenched.
Regarding your specific points:
1) The "chaos control" literature is supposed to deal
with this and is very active. The econ applications of
this are way behind and often pretty stupid. In physics
it is really getting somewhere, especially in the area
of celestial mechanics (controlling spacecraft) and
in signals management.
2) "Reduction of dimension"? All of complex dynamics?
Certainly in the empirical chaos lit there has been a
failure to find much in the way of low dimensional
deterministic chaos. Is this what you are referring to?
In other areas, e.g., catastrophe theory models of
species collapse and extinction from overharvesting,
there is certainly a low enough dimensionality in some
models to be very useful.
3) Do you mean"fractal" or "fractional," although these
are certainly related. This stuff is still be studied and
used in time series analysis, especially for long memory
stuff, which also appears to be there in a lot of
financial time series.
Barkley Rosser
----- Original Message -----
From: "Les Schaffer" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Thursday, June 19, 2003 7:11 AM
Subject: Re: [PEN-L] Complexity
> Barkley wrote:
>
> > I think Ralph Abraham is a genius.
>
> i liked his cartoon books on dynamics very much. it was his text w/
> Marsden and Ratiu that puts me to sleep.
>
> > He also discovered "chaotic hysteresis," although I am the one who
> > coined that term.
>
> can you send me your paper on this offlist, it sounds interesting? the
> one on your wesbite has no figures.
>
> other bubbles which have subsided some:
>
> 1.) chaos theory was going to point the way to a "solution" to
> turbulence. hasn't happened yet.
>
> 2.) complex dynamics projected onto low dimensional subspaces: nice
> idea, havent seen any actual implementation in a problem which begs
> for reduction of dimension.
>
> 3.) fractional dimension fad: there was a time when everyone
> published a fractional dimension for their time series. what was
> that supposed to prove???
>
> les schaffer
>
