Amorphic complexity, introduced in 2016, is a new topological invariant of discrete dynamical systems that is of particular interest for systems of entropy zero. Examples exist that show that amorphic complexity can take values 0 and 1 or more (inlcuding infinity), but it was not known if values from the interval (0,1) could be taken. This note proves that for every real nonnegative number there exists a noncomplete metric space and a map on it that has amorphic complexity equal to this number. The construction makes strong use of incompleteness of the space and the question whether these values can be realized for a map on a compact metric space remains open.

2016年引入的非晶态复杂性是离散动力学系统的一种新拓扑不变式，这对于熵零系统尤为重要。存在的示例表明，非晶复杂性可以采用0和1或更大的值（包括无穷大），但是尚不清楚是否可以采用间隔（0,1）中的值。该注释证明，对于每个实非负数，都存在一个不完整的度量空间，并且其上的一个映射具有等于此数字的非晶复杂性。该结构充分利用了空间的不完整性，对于在紧凑的度量空间上的地图是否可以实现这些值的问题仍然存在。