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arXiv · 0802.0520

Multifractal analysis of Birkhoff averages on "self-affine" symbolic spaces

Julien Barral·Mounir Mensi
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Abstract

We achieve on self-affine Sierpinski carpets the multifractal analysis of the Birkhoff averages of potentials satisfying a Dini condition. Given such a potential, the corresponding Hausdorff spectrum cannot be deduced from that of the associated Gibbs measure by a simple transformation. Indeed, these spectra are respectively obtained as the Legendre transform of two distinct concave differentiable functions that cannot be deduced from one another by a dilation and a translation. This situation is in contrast with what is observed in the familiar self-similar case. Our results are presented in the framework of almost-multiplicative functions on products of two distinct symbolic spaces and their projection on the associated self-affine carpets.

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Julien Barral, Mounir Mensi. 2008-02-04. Multifractal analysis of Birkhoff averages on "self-affine" symbolic spaces. https://doi.org/10.1088/0951-7715%2F21%2F10%2F011

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