  Let $M$ be a three-dimensional contact manifold and $\psi:D\setminus\{0\}\to
M\times{\Bbb R}$ a finite-energy pseudoholomorphic map from a punctured disc in
${\Bbb C}$, that is asymptotic to a periodic orbit of the Reeb vector field.
This article examines conditions under which smooth coordinates may be defined
in a tubular neighbourhood of the orbit such that $\psi$ resembles a
holomorphic curve, invoking comparison with the theory of topological linking
of plane complex algebroid curves near a singularity. Examples of this
behaviour which are studied in some detail include pseudoholomorphic maps into
${\Bbb E}_{p,q}\times{\Bbb R}$, where ${\Bbb E}_{p,q}$ denotes a rational
ellipsoid with contact structure induced by the complex structure of the
ambient ${\Bbb C}^{2}$. Contact structures arising from non-standard
circle-fibrations of the three-sphere are also examined.
