Also, instead of having the infinitely long time series considered by Takens one works in practice with a time series of finite length (from which we construct a series of vectors with the method of delays), so we need to find a criterion for the smallest number of data points required to get ``good'' results.

Takens' theory does not say anything about the sampling time between two successive measurements. (It has not been necessary so far to say something about it, because for generically any value of can be taken.) For a real data set is finite, so we cannot expect any more that every sampling time will give good results. We must assign a suitable value to .

Additionally, all data, no matter if it is taken from numerical or physical experiments, will be noisy (i.e. it will be measured with finite precision only) and we must consider this problem when building our strategy of data analysis.

- Basic Remarks about the Choice of Embedding Dimension and Sampling Time
- Topological Considerations
- An Algorithm based on the Calculation of the Correlation Dimension
- Singular System Analysis
- On the Required Number of Data Points