  Using a combination of analytical and numerical techniques, we show that
chaos in globally-coupled identical dynamical systems, be they dissipative or
Hamiltonian, is both extensive and sub-extensive: their spectrum of Lyapunov
exponents is asymptotically flat (thus extensive) at the value $\lambda_0$
given by a single unit forced by the mean-field, but sandwiched between
sub-extensive bands containing typically $\mathcal{O}(\log N)$ exponents whose
values vary as $\lambda \simeq \lambda_\infty + c/\log N$ with $\lambda_\infty
\neq \lambda_0$.
