多分形测度的正则系综描述

Canonical ensemble description of multifractal measure

借助多分形公式与热力学、统计物理学间的类比关系，建立了多分形测度的正则系综描述．根据系综理论，证明了多分形测度的ｑ阶矩等于相应正则系综的配分函数．这为发展多分形理论。

Using the analogy relation between multifractal formula and thermodynamics and statistical physics, a canonical ensemble of multifractal measure has been estiblished. It has been proved that the q th momentum of multifractal measure is the same as the partition function of the corresponding ensenmble in terms of canonical ensemble theory. It may provide another way to develope the statitical physics theory of multifractal.