The topology of fluid flow past a sequence of cylinders
This paper and an earlier, more physically oriented paper by the same authors [Chaos 7, No. 1, 125-138 (1997; Zbl 0967.76546)], treat a periodic differential equation in the plane. The differential equation models a fluid flow around a sequence of circular obstacles put with equidistant gaps along the \(x\)-axis. The flow is laminar some distance away from the \(x\)-axis. Based on numerical observations in this model, a number of properties for the period-map are assumed to hold. In particular, it is assumed that the period map possesses hyperbolic horseshoes in between consecutive obstacles. The unstable manifold of one such horseshoe is supposed to intersect the stable manifold of the horseshoe between the next obstacles. The structure of invariant sets and their unstable manifolds is described. Corresponding results are derived for systems with noise added. The set of points whose flow lines stay to the right of the starting point is proved to contain an indecomposable continuum.
periodic differential equation in the plane
scientific article; zbMATH DE number 1317232