  Six-dimensional Einstein-Gauss-Bonnet gravity (with a linear Gauss-Bonnet
term) is investigated. This theory is inspired by basic features of results
coming from string and M-theory. Dynamical compactification is carried out and
it is seen that a four-dimensional accelerating FRW universe is recovered, when
the two-dimensional internal space radius shrinks. A non-perturbative structure
of the corresponding theory is identified which has either three or one stable
fixed points, depending on the Gauss-Bonnet coupling being positive or
negative. A much richer structure than in the case of the perturbative regime
of the dynamical compactification recently studied by Andrew, Bolen, and
Middleton is exhibited.
