  We consider an inverse spectral problem for a class of singular AKNS
operators $H\_a, a\in\N$ with an explicit singularity. We construct for each
$a\in\N$, a standard map $\lambda^a\times\kappa^a$ with spectral data
$\lambda^a$ and some norming constant $\kappa^a$. For $a=0$,
$\lambda^a\times\kappa^a$ was known to be a local coordinate system on
$\lr\times\lr$. Using adapted transformation operators, we extend this result
to any non-negative integer $a$, give a description of isospectral sets and we
obtain a Borg-Levinson type theorem.
