next up previous contents
Next: The ``hypercube'' Up: THE CORRELATION INTEGRAL Previous: Methods for estimating the   Contents

Two analytical examples

Even in the case of noise-free data the dimension estimates will have a systematic error due to, for example, lack of self-similarity. Furthermore, we have to estimate the dimension at distances greater than zero, for which the relation $C(r) \sim r^{D_q}$ does not exactly hold. This is another source of systematic errors, as will be demonstrated by the following two analytical examples. Numerical examples can be found in Chapters 3, 5 and 7.