The packing spectrum for Birkhoff averages on a self-affine repeller
arXiv:1006.4086
Abstract
We consider the multifractal analysis for Birkhoff averages of continuous potentials on a self-affine Sierpiński 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 Hölder 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.
arXiv comment25 pages, 2 figures; to appear in Ergodic Theory & Dynamical Systems