  The apparent difficulty in recovering classical nonlinear dynamics and chaos
from standard quantum mechanics has been the subject of a great deal of
interest over the last twenty years. For open quantum systems - those coupled
to a dissipative environment and/or a measurement device - it has been
demonstrated that chaotic-like behaviour can be recovered in the appropriate
classical limit. In this paper, we investigate the entanglement generated
between two nonlinear oscillators, coupled to each other and to their
environment. Entanglement - the inability to factorise coupled quantum systems
into their constituent parts - is one of the defining features of quantum
mechanics. Indeed, it underpins many of the recent developments in quantum
technologies. Here we show that the entanglement characteristics of two
`classical' states (chaotic and periodic solutions) differ significantly in the
classical limit. In particular, we show that significant levels of entanglement
are preserved only in the chaotic-like solutions.
