Chaos and Ergodicity in the One and Two Dimensional Dripping Handrail Models

The Dripping Handrail Model (DHR) is a discrete dynamical system used to model a binary star system in which matter accretes off of one star onto the other. With this model, we study the behavior of the matter as it collects in a ring around the star, called an accretion disc, builds up, and eventually drips onto the surface of the star. Considering the accretion disc as both a one dimensional and two dimensional “rail” divided into discrete cells, we investigate numerical evidence of chaotic behavior on a certain invariant subset, and ergodic behavior of the system as a whole. Subject headings: binary star system; accretion disc; chaotic; ergodic; invariant subset