  Symplectic Field Theory studies J-holomorphic curves in almost complex
manifolds with cylindrical ends. One natural generalization is to replace
'cylindrical' by 'asymptotically cylindrical'. In this article, we generalize
the asymptotic results about the behavior of J-holomorphic curves near infinity
to the asymptotically cylindrical setting. We also sketch how these asymptotic
results allow the main compactness theorems in Symplectic Field Theory proved
by Bourgeois, Eliashberg, Hofer, Wysocki and Zehnder to be extended to the
asymptotically cylindrical case.
