  We study a parametric version of the Kannan-Lipton Orbit Problem for linear
dynamical systems. We show decidability in the case of one parameter and
Skolem-hardness with four or more parameters.
  More precisely, consider $M$ a d-dimensional square matrix whose entries are
rational functions in one or more real variables. Given initial and target
vectors $u,v \in \mathbb{Q}^d$, the parametrised point-to-point reachability
problem asks whether there exist values of the parameters giving rise to a
concrete matrix $N \in \mathbb{R}^{d\times d}$, and a positive integer $n$,
such that $N^n u = v$.
  We show decidability in the case where $M$ depends only upon a single
parameter, and we exhibit a reduction from the well-known Skolem problem for
linear recurrence sequences, indicating intractability in the case of four or
more parameters.
