We study the influence of eddies detaching from a jet on intergyre transport in 
a model consisting of a three layer quasigeostrophic flow in a square domain 
subject to a sinusoidal in space (constant in time) wind stress that leads to 
the double gyre configuration. We use techniques from dynamical systems theory 
to study intergyre transport. In particuliar distinguished hyperbolic 
trajectories (DHT's) along with their stable and unstable manifolds are computed 
in order to implement the technique of lobe dynamics. An unstable manifold 
associated with a DHT on the western boundary and a stable manifold associated 
with a DHT on the eastern boundary are computed. These manifolds control 
intergyre transport. The influence of detached eddies on intergyre transport can 
then be determined by studying their influence on these stable and unstable 
manifolds. These eddies also have associated DHT's with their own stable and 
unstable manifolds. These are computed in order to understand their interaction 
with the unstable and stable manifolds on the boundaries controlling intergyre 
transport as well as to study the flux between the eddies and the main flow. 
Bifurcations of the stagnation points associated with the eddies complicate the 
computation of the DHT's. Special cases of bifurcations are studied and the 
issue of the existence of a DHT during a bifurcation of stagnation points is 
outlined.