测度熵计算中映射不变分布的应用

APPLICATION OF MAPPING INVARIANT DISTRIBUTION TO CALCULATING MEASURE THEORETIC ENTROPY

构造计算测度熵（ＭｅｔｒｉｃＥｎｔｒｏｐｙ）的马尔可夫划分（ＭａｒｋｏｖＰａｒｔｉｔｉｏｎ）时，对于非线性映射采取等似然假设，影响精度。提出用计算映射的不变分布来进行改进；对逻辑映射导出映射不变分布的算式及迭代格式，进行了测度熵的计算；计算表明，迭代次数不多时即能得出较好结果。

An improvement of constituting Markov partition is proposed for calculating measure theoretic entropy by computing invariant distribution of nonlinear mapping instead assuming equal likelihood for all points over a interval; and the formulations and the iteration forms of invariant distribution of logistic map are derived.It is shown that the better result can be obtained through several iterations and the amount of computation is not larger.