Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers
Dynamical Systems
2011-03-25 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1008.0301,
title = {Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers},
author = {Henry WJ Reeve},
journal= {arXiv preprint arXiv:1008.0301},
year = {2011}
}
Comments
22 pages, 1 figure