非一致扩张 $C^1$ 映射的弱 Gibbs 测度的多重分形分析
动力系统
2009-08-14 v3
摘要
我们考虑 Manneville-Pomeau 型 非一致双曲系统上弱 Gibbs 测度的局部维数谱。我们利用不变测度、一致双曲遍历测度和平衡态三种方式给出该谱。在附加假设下，我们还证明了该谱的解析性。这三种表述对于光滑一致双曲系统而言是众所周知的。
引用
@article{arxiv.0806.0727,
title = {Multifractal analysis of weak Gibbs measures for non-uniformly expanding C^1 maps},
author = {Thomas Jordan and Michal Rams},
journal= {arXiv preprint arXiv:0806.0727},
year = {2009}
}
备注
New version, main changes: the results hold for continuous potentials (previously: Holder potentials) and C^1 maps (previously: C^1+\alpha), we also prove analyticity of the spectrum