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

Published online by Cambridge University Press:  08 September 2011

HENRY W. J. REEVE
HENRY W. J. REEVE*
Affiliation:
Department of Mathematics, The University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK (email: henrywjreeve@googlemail.com)
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Abstract

We consider the multifractal analysis of Birkhoff averages of continuous potentials on a self-affine Sierpiński sponge. In particular, we give a variational principle 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 4 , August 2012 , pp. 1444 - 1470
Copyright
Copyright © Cambridge University Press 2011

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