  We completely classify fixed point subgroups in Torus Knot Groups, that is
groups of the form $G_{p,q} = \langle x , y | x^p = y^q \rangle$. We not only
give the isomorphism type, but also the explicit generators for the fixed point
subgroup of each automorphism of $G_{p,q}$. Our main tool is an action of
$Aut(G_{p,q})$ on the Bass-Serre tree of $G_{p,q}$ which is compatible with the
original action, in the sense that it extends the original action of $G_{p,q}$
on its Bass-Serre tree.
