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Hausdorff spectrum of Lyapunov exponents for higher-dimensional self-affine systems
Abstract
We study the Hausdorff dimension of projections of level sets of Lyapunov exponents for affine iterated function systems. Assuming that the tuple of linear parts is typical, we obtain a variational formula in terms of pressure, topological entropy, and the Lyapunov dimensions of invariant measures corresponding to Lyapunov exponents. In ℝ3, we show that this value equals the Hausdorff dimension of the canonical projection of the level set under the strong open set condition. We further extend the result to arbitrary dimensions, showing that the same formula holds for Lebesgue-almost every choice of translation vectors under a suitable contraction assumption.
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BibTeX
@misc{barany2026hausdorff,
title = {{Hausdorff spectrum of Lyapunov exponents for higher-dimensional self-affine systems}},
author = {Balázs Bárány and Reza Mohammadpour},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19309},
eprint = {2609.19309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19309},
}
RIS
TY - UNPB
TI - Hausdorff spectrum of Lyapunov exponents for higher-dimensional self-affine systems
AU - Balázs Bárány
AU - Reza Mohammadpour
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19309
UR - https://arxiv.org/abs/2609.19309
AB - We study the Hausdorff dimension of projections of level sets of Lyapunov exponents for affine iterated function systems. Assuming that the tuple of linear parts is typical, we obtain a variational formula in terms of pressure, topological entropy, and the Lyapunov dimensions of invariant measures corresponding to Lyapunov exponents. In ℝ^3, we show that this value equals the Hausdorff dimension of the canonical projection of the level set under the strong open set condition. We further extend the result to arbitrary dimensions, showing that the same formula holds for Lebesgue-almost every choice of translation vectors under a suitable contraction assumption.
ER -