The calculation approach of the nearest neighbor distance of chaotic time series's reconstructed space

For the rapid develop of computer speed, the small calculating advantage of ∞-norm is gone when the nearest points of chaotic time series's reconstructed space are found by 2-norm or ∞-norm. So the right method should be selected on the basis of reconsidered the two methods. By theories analysis, the ratio between ∞-norm distance and 2-norm distance is in an inherent interval. Huanan Zhixin and Lorenz data are used for verified the effect of finding the nearest points by the two norms. The nearest points is partly the same by the two norms and the found same point rate is different between two time series. And the nearest distance calculating by 2-norm between the point pair finding by ∞-norm is equal or great than the point pair finding by 2-norm. So the real nearest point is found by 2-norm.