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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-1-5,
author = {Henry W. J. Reeve},
title = {Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {71-93},
zbl = {1230.37034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-1-5}
}
Henry W. J. Reeve. Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers. Fundamenta Mathematicae, Tome 215 (2011) pp. 71-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-1-5/