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

Henry WJ Reeve

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arXiv · 1006.4086

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

Henry WJ Reeve

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Abstract

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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Henry WJ Reeve. 2010-06-21. The packing spectrum for Birkhoff averages on a self-affine repeller. https://arxiv.org/abs/1006.4086

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