Suppose I have two discrete long-time series from two dynamical systems. I assume these two systems have compact attractor. How do I measure the closeness or distinctness of the two attractors from the two time series? It is possible that these two attractors are disjoint. In that case I hope the measure still can tell how much they are apart from each other. Any suggestion is appreciated. 



How to quantify the closeness/distinctness of the attractors?
The Hausdorff distance between two sets $A,B$ is defined by
$$
d\_H(A,B)=\inf\_{\epsilon>0}\big((\forall a\in A\exists b\in B : d(b,a)<\epsilon) \& (\forall b\in B\exists a\in A : d(a,b)<\epsilon)\big).
$$
It is often used to measure distances between compact subsets of a metric space.


