  In order to study the chaotic behavior of a system with non-local
interactions, we will consider weakly coupled non-commutative field theories.
We compute the Lyapunov exponent of this exponential growth in the large
Moyal-scale limit to leading order in the t'Hooft coupling and $1/N$. We found
that in this limit, the Lyapunov exponent remains comparable in magnitude to
(and somewhat smaller than) the exponent in the commutative case. This can
possibly be explained by the infrared sensitivity of the Lyapunov exponent.
Another possible explanation is that in examples of weakly coupled
non-commutative field theories, non-local contributions to various
thermodynamic quantities are sub-dominant.
