Dynamical Systems Seminar

Bob Devaney defines a dynamical system (generated by a map or a differential equation) to be chaotic if (a) it is topologically transitive, (b) if the periodic points are dense and (c) if it has sensitive dependence on initial conditions. We extend Devaney's notion of chaos to the context of continuous actions of topological semigroups. A very nice result of Banks et al. shows that the condition (c) of being sensitive to initial conditions is redundant. We generalize this result to chaotic actions of topological semigroups. This is joint work with Friedrich M. Schneider, Sebastian Kerkhoff and Mike Behrisch.