The equivalent of an attractor in general relativity is simply a black
hole. It is hypothesized that a black hole contains a singularity, but the
black hole itself extends far beyond it. A black hole is an attractor by
definition of the concept "attractor": a region you can enter but not
leave. This means that the dynamics of general relativity allows for
intrinsic irreversibility: the movement of falling into an attractor cannot
be reversed.
This is unlike Newtonian mechanics where all movements are reversible,
since the dynamics does not make any intrinsic difference between past and
future. Since relativity theory is derived from Newtonian mechanics it is
rather surprising to find that it implies irreversibility. Quantum
mechanics, for example, which is also a generalization of Newtonian
mechanics is reversible (at least its dynamics described by the
Schroedinger equation), and therefore does not allow for attractors.
>There must be some literature on
>this, I would expect, since resolution of orbital dynamics using the
>Newtonian view becomes quite complex after a small number of interacting
>bodies, and is certainly simpler (but not as rigorously predictive) to
>describe it in terms of chaos.
Please note that the existence of attractors is independent of the
existence of chaos (i.e. sensitive dependence on initial conditions): you
can have the one without the other. Newtonian mechanics does allow chaos,
but not attractors. To have a "strange" attractor, though, you need both.
_________________________________________________________________________
Francis Heylighen <fheyligh@vub.ac.be> -- Center "Leo Apostel"
Free University of Brussels, Krijgskundestr. 33, 1160 Brussels, Belgium
tel +32-2-6442677; fax +32-2-6440744; http://pespmc1.vub.ac.be/HEYL.html