Multifractal analysis for Birkhoff averages on Lalley–Gatzouras repellers

Volume 212 / 2011

Henry W. J. Reeve Fundamenta Mathematicae 212 (2011), 71-93 MSC: Primary 37C45. DOI: 10.4064/fm212-1-5


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.


  • Henry W. J. ReeveDepartment of Mathematics
    The University of Bristol
    University Walk
    Clifton, Bristol, BS8 1TW, UK

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