Abstract: The fixed points in logistic mapping digital-flow chaos strange attractor are studied in detail. When k=n in logistic equation, there exist no more than 2n fixed points, which are deduced and proved theoretically. Three corollaries about the fixed points of logistic mapping are proposed and proved respectively. These theoretn and corollaries provide a theoretical basis for choosing parameter of chaotic sequences in chaotic secure communication and chaotic digital watermarking. And they are testified by simulation.