Chaos in the dynamics generated by sequences of maps, with applications to chaotic advection in flows with aperiodic time dependence
This paper is concerned with chaos in the dynamics generated by infinite sequences of maps. In particular, it is concerned with the invariant sets on which the dynamics is equivalent to some type of symbolic dynamics and has sensitive dependence on initial conditions. The classical approach for proving the existence of such sets utilizes the Conley-Moser conditions. In this paper the author generalizes these conditions to the situation when the dynamics is generated by an infinite sequence of maps. From these new conditions results are derived describing chaos when there is only positive evolution and finite time or transient chaos. It is to be noted that the methods developed in the paper do not require the existence of a homoclinic orbit in order to prove the existence of chaotic dynamics. The obtained results are applied to several examples in fluid mechanics. Each of these examples is modeled as a type of ``blinking flow'', which mathematically has the form of linked twist map or an infinite sequence of linked twist maps. It is shown that the nature of these blinking flows such that it is possible to have a variety of ``patches'' of chaos in the flow corresponds to different length and time scales.
scientific article; zbMATH DE number 1340254