自仿射系统的维数最大化测度
动力系统
2016-04-27 v4
摘要
本文研究线性部分满足支配分裂和强分离条件的平面自仿射集的维数理论。本文的主要结果是维数最大化 Gibbs 测度（Käenmäki 测度）的存在性。为证明这一现象，我们证明了 Ledrappier-Young 公式对 Gibbs 测度成立，并引入了射影空间上强稳定方向的横截性条件。
引用
@article{arxiv.1507.02829,
title = {Dimension maximizing measures for self-affine systems},
author = {Balázs Bárány and Michał Rams},
journal= {arXiv preprint arXiv:1507.02829},
year = {2016}
}
备注
The previous version of the paper has been withdrawn by the author due to a crucial error. It was in the previous version in Section 4, Lemma 4.6 equation (4.4). This error annihilated Theorem 1.2