The \emph{Orbit problem} is defined as follows: Given a matrix
A\in \Q ^{n\times n} and vectors \x,\y\in \Q ^n, does there exist a
non-negative integer i such that A^i\x=\y. This problem was
shown to be in deterministic polynomial time by Kannan and Lipton in
\cite{KL1986}. In this paper we place the problem in the logspace
counting hierarchy \GapLH. We also show that the problem is hard
for \CeqL with respect to logspace many-one reductions.

The \emph{Orbit problem} is defined as follows: Given a matrix A\in \Q ^{n\times n} and vectors \x,\y\in \Q ^n, does there exist a
non-negative integer i such that A^i\x=\y. This problem was
shown to be in deterministic polynomial time by Kannan and Lipton in
\cite{KL1986}. In this paper we place the problem in the logspace
counting hierarchy \GapLH. We also show that the problem is hard
for \L under \NCone-many-one reductions.