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

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

2010-06-21

arxiv.org/abs/1006.4086v2

Mathematics

Dynamical Systems

25 pages, 2 figures; to appear in Ergodic Theory & Dynamical Systems

Scientific paper

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.

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