ABSTRACT
The ergodic problem of statistical mechanics is the problem of justifying the replacement of time averages of observables by their phase space averages. This amounts to the problem of showing that a given measure preserving dynamical system is ergodic. Relatively few techniques exist for this purpose. In the topological study of dynamical systems the object is to study the phase portrait or orbit structure of the problem. Features of a dynamical system such as the existence of periodic orbits which are of topological interest may not be of statistical interest because they may occur with probability zero. Linked twist mappings provide a class of dynamical systems with interesting topological and statistical properties. The study of linked twist maps incorporates some of the difficulties associated with studying so called “ergodic zones” in celestial mechanics.
