🚀 go-pugleaf

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,

No I don't think so.  I believe there is little discussion of Hamiltonian
or conservative systems in that review.  

It is now well known that typical physical chaotic models (not the tent-map)
have a wide variation in their finite-time Lyapunov exponents, and therefore
finite-time dynamical predictability.

: and my
: interest is in dissipative systems, with changing dimension and
: transients. 

Nonstationarity or driven inputs, however, does add something new.  And you
need a model. 

:Back in 1990, I was already wrestling with this, and in my
: paper for the Cambridge Conference, I proposed to use topological
: properties to characterize these systems. For example, one of the key
: concerns of peer polity elites was maintaining constant dimension, since
: 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.

what is 'peer polity elites'?

You might be interested in things like "chaotic repellers"
and "deterministic noise amplifiers": chaotic systems with small stochastic
inputs which get amplified.  Really like that fabled "butterfly effect".

See, e.g.

R.J. Deissler, and J. D. Farmer, Physica D 55 155-165 (1992).

: --
: Harry Erwin
: Internet: herwin@gmu.edu 
: Working on Katchalsky nets....

--
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