Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers

Details Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers

2010-08-02

arxiv.org/abs/1008.0301v2

Fund. Math. 212 (2011), 71-93

Mathematics

Dynamical Systems

22 pages, 1 figure

Scientific paper

We consider the multifractal analysis for Birkhoff averages of continuous potentials on a class of non-conformal repellers corresponding to the self-affine limit sets studied by Lalley and Gatzouras. A conditional variational principle is given for the Hausdorff dimension of the set of points for which the Birkhoff averages converge to a given value. This extends a result of Barral and Mensi to certain non-conformal maps with a measure dependent Lyapunov exponent.

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