Abstract: Based on the some differential dynamic systems of known control equations, it is found that there existed some essential problems in estimating the fractal dimensions of attractors with one dimensional time series. by a comparison between the two fractal dimension results of the reconstructed phase-space,which is made according to their solution series of different components and different time intervals, and of the original phase-space. Some significant facts are found. Then, the theory of reconstructed phase-space with one dimensional time series is discussed and some essential problems exited in it are found. Finally, it should be pointed out that the real, reliable, useful resuits would be obtained only when the clear understanding of what kind of the delay time r and the sample interval H are used in a single-variable of the dynamic system to keep the same measure nature between the reconstructed phase-space and the original phase-space.