  In this paper cosmological dynamics in Einstein-Gauss-Bonnet gravity with a
perfect fluid source in arbitrary dimension is studied. A systematic analysis
is performed for the case that the theory does not admit maximally symmetric
solutions. Considering two independent scale factors, namely one for the three
dimensional space and one for the extra dimensional space, is found that a
regime exists where the two scale factors tend to a constant value via damped
oscillations for not too negative pressure of the fluid, so that asymptotically
the evolution of the $(3+1)$-dimensional Friedmann model with perfect fluid is
recovered. At last, it is worth emphasizing that the present numerical results
strongly support a 't Hooft-like interpretation of the parameter $1/D$ (where
$D$ is the number of extra dimensions) as a small expansion parameter in very
much the same way as it happens in the large $N$ expansion of gauge theories
with $1/N$. Indeed, the dependence on $D$ of many of the relevant physical
quantities computed here manifests a clear WKB-like pattern, as expected on the
basis of large $N$ arguments.
