Geodesic
Multifractal analysis for Birkhoff averages on Lalley–Gatzouras repellers
Henry W. J. Reeve 1
1 Department of Mathematics The University of Bristol University Walk Clifton, Bristol, BS8 1TW, UK
Fundamenta Mathematicae, Tome 212 (2011) no. 1, pp. 71-93 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm212-1-5
Keywords: consider multifractal analysis birkhoff averages continuous potentials class non conformal repellers corresponding self affine limit sets studied lalley gatzouras conditional variational principle given hausdorff dimension set points which birkhoff averages converge given value extends result barral mensi certain non conformal maps measure dependent lyapunov exponent

Henry W. J. Reeve  1

1 Department of Mathematics The University of Bristol University Walk Clifton, Bristol, BS8 1TW, UK 
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Henry W. J. Reeve. Multifractal analysis for Birkhoff averages on Lalley–Gatzouras repellers. Fundamenta Mathematicae, Tome 212 (2011) no. 1, pp. 71-93. doi: 10.4064/fm212-1-5

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