Digraph Mapping Properties
by
John Banks
School of Mathematical and Statistical Sciences, La Trobe University

Topological transitivity, weak mixing and non-wandering describe ways in which open sets feed into each other under iteration of maps. Using finite directed graphs, a general class of properties that includes these three will be defined and the extent to which they are logically distinct will be considered. It turns out that there are only three distinct properties which entail ``interesting'' dynamics and there is a countably infinite collection of properties entailing somewhat less interesting dynamics.

Date received: June 20, 2002