This issuePrevious ArticleStability of symmetric periodic solutions with small amplitude of $\dot x(t)=\alpha f(x(t), x(t-1))$Next ArticleLarge time behavior of solutions to the generalized derivative nonlinear Schrödinger equation
Topological mapping properties defined by digraphs
Topological transitivity, weak mixing and non-wandering are definitions used
in topological dynamics to describe the ways in which open sets feed into each other under
iteration. Using finite directed graphs, these definitions are generalized to obtain topological
mapping properties. The extent to which these mapping properties are logically distinct is
examined. There are three distinct properties which entail "interesting" dynamics. Two
of these, transitivity and weak mixing, are already well known. The third does notappear
in the literature but turns out to be close to weak mixing in a sense to be discussed. The
remaining properties comprise a countably infinite collection of distinct properties entailing
somewhat less interesting dynamics and including non-wandering.