Mendes France与分形谱：收缩分形过程与扩张分形过程的比较研究
Mendes France and thermodynamical spectra: a comparative study of contractive and expansive fractal processes
摘要：
本文对R（n）中的两类曲线进行了比较研究。第一种是由压缩过程得到的自相似有界分形，并且具有非整数的Hausdorff维数。第二类是无界的，局部可求长的，局部光滑的，由扩张过程得到的，并由M定义的分数维来刻画。法国门德斯。我们提出了一种方法来联系这两种类型的曲线和它们各自的非整数维。因此，一个分形有界曲线，我们相关联的，首先，一个有限范围的门德斯法国维，确定最小和最大的。后来，我们表明，这种离散谱可以连续，使其与文献中遇到的其他一些多重分形谱进行比较。我们讨论相应的物理解释。
英文摘要：
This paper presents a comparative study of two families of curves in R(n). The first ones comprise self-similar bounded fractals obtained by contractive processes, and have a non-integer Hausdorff dimension. The second ones are unbounded, locally rectifiable, locally smooth, obtained by expansive processes, and characterized by a fractional dimension defined by M. Mendes France. We present a way to relate the two types of curves and their respective non-integer dimensions. Thus, to one fractal bounded curve we associate, at first, a finite range of Mendes France dimensions, identifying the minimal and the maximal ones. Later, we show that this discrete spectrum can be made continuous, allowing it to be compared with some other multifractal spectra encountered in the literature. We discuss the corresponding physical interpretations.
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