探讨了分形测度小波变换极大值线的拓扑分岔情况，并提出了一种基于小波变换模极大值的多重分形谱估算方法。
Topologic bifurcation situation of maxima lines is also discussed. In the end, an estimation for multifractal spectrum is proposed in terms of wavelet module maxima lines.
本文从分形信息论观点出发，考察多重测度分形，导出基于分形熵比的多重分形维谱函数。
From the view of fractal information theory, the multifractal has been introduced, and the multifractal dimension spectrum function based on the fractal entropy has been investigated.
其中第一章是关于度量空间中的图定向自相似集合，第二章是关于动力系统中平衡态测度的重分形分析。
The first chapter is about graph-directed self-similar sets in complete metric spaces, and the second chapter is about multifractal analysis of equilibrium measures in dynamical systems.
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