From the abstract: The study of numerical methods for initial value problems by considering their approximation properties from a dynamical systems viewpoint is now a well-established field; a substantial body of knowledge, developed over the past two decades, can be found in the literature. Nonetheless many open questions remain concerning the meaning of long-time simulations performed by approximating dynamical systems. In recent years various attempts to analyse the statistical content of these long-time simulations have emerged, and the purpose of this article is to review some of that work. The subject area is far from complete; nonetheless a certain unity can be seen in what has been achieved to date and it is therefore of value to give an overview of the field.
For the entire collection see [Zbl 0962.00005].