Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers

被引：8

作者：

Reeve, Henry W. J. ^{[1
]}

机构：

[1] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England

来源：

FUNDAMENTA MATHEMATICAE | 2011年 / 212卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Birkhoff averages; multifractal analysis; non-conformal; dimension theory; Hausdorff dimension; Lalley-Gatzouras; HAUSDORFF DIMENSION; SIERPINSKI CARPETS; DIVERGENCE POINTS; SYSTEMS; ENTROPY; SPECTRA; SETS;

D O I：

10.4064/fm212-1-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：71 / 93

页数：23

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