Omega-limit sets, Chain Transitivity and Symbolic Dynamics

Abstract: Omega-limit sets are important objects in the study of discrete dynamical systems, in that they tell us a great deal about the asymptotic behaviour of the orbits of points. Furthermore, they have many interesting dynamical properties, one of which is that of internal chain transitivity, which is related to computer-based numerical analysis.Using symbolic dynamics as well as traditional analysis, and focusing our attention on tent maps, we investigate the cases for which being an omega-limit set is identical to having internal chain transitivity."