The topology of fluid flow past a sequence of cylinders

This paper analyzes conditions under which dynamical systems in the plane have indecomposable continua or even infinite nested families of indecomposable continua. Our hypotheses are patterned after a numerical study of a fluid flow example, but should hold in a wide variety of physical processes. The basic fluid flow model is a differential equation in R2 which is periodic in time, and so its solutions can be represented by a time-1 map F:R2→R2. We represent a version of this system “with noise” by considering any sequence of maps Fn:R2→R2, each of which is ε-close to F in the C1 norm, so that if p is a point in the fluid flow at time n, then Fn(p) is its position at time n+1. We show that indecomposable continua still exist for small ε.