We consider the multifractal analysis for Birkhoff averages of continuous
potentials on a self-affine Sierpi\'{n}ski sponge. In particular, we give a
variational principal for the packing dimension of the level sets. Furthermore,
we prove that the packing spectrum is concave and continuous. We give a
sufficient condition for the packing spectrum to be real analytic, but show
that for general H\"{o}lder continuous potentials, this need not be the case.
We also give a precise criterion for when the packing spectrum attains the full
packing dimension of the repeller. Again, we present an example showing that
this is not always the case.Comment: 25 pages, 2 figures; to appear in Ergodic Theory & Dynamical System
