The packing spectrum for Birkhoff averages on a self-affine repeller

摘要

We consider the multifractal analysis for Birkhoff averages of continuouspotentials on a self-affine Sierpi\'{n}ski sponge. In particular, we give avariational principal for the packing dimension of the level sets. Furthermore,we prove that the packing spectrum is concave and continuous. We give asufficient condition for the packing spectrum to be real analytic, but showthat 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 fullpacking dimension of the repeller. Again, we present an example showing thatthis is not always the case.