Multifractal analysis for Birkhoff averages on Lalley–Gatzouras repellers
Volume 212 / 2011
Fundamenta Mathematicae 212 (2011), 71-93
MSC: Primary 37C45.
DOI: 10.4064/fm212-1-5
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.
