可数Markov映射的Birkhoff和商的多重分形分析
动力系统
2018-09-18 v2
摘要
本文致力于研究可数Markov映射的Birkhoff平均商的多重分形分析。我们证明了水平集Hausdorff维数的变分原理。在某些假设下，我们能够证明谱在其定义域的部分区域上解析变化。我们将结果应用于Manneville-Pomeau映射，表明其Birkhoff谱可能不连续，显示出与一致双曲情形显著不同的差异。我们还得到了描述悬链流Birkhoff谱的结果。文中还给出了涉及连分数的例子。
引用
@article{arxiv.1303.2596,
title = {Multifractal analysis for quotients of Birkhoff sums for countable Markov maps},
author = {Godofredo Iommi and Thomas Jordan},
journal= {arXiv preprint arXiv:1303.2596},
year = {2018}
}
备注
New version, now with 28 papers. Much more detail is now given in section 4. We've also corrected a few typos and added some additional explanation to some of the proofs (e.g. prop 6.1)