Resampling and estimation of correlation dimension and largest Lyapunov exponent

Estimation of invariants plays a very important role in the analysis of chaotic time series. However, the length of tune series affects the quality of estimation directly. To estimate these invariants accurately, the length of time series must be very long, especially for the continuous chaotic systems. On the condition of keeping the total observation time-constant, the method of resampling is introduced to the analysis of chaotic time series, experimental results and corresponding analysis indicate that resampling can keep the good quality of original phase space, and reduce the total computation time quickly. This may be an efficient method to calculate the invariants of chaotic system by shortening time series.