On the Mandelbrot set for pairs of linear maps

A Mandelbrot set for pairs of complex linear maps was introduced by Barnsley and Harrington in 1985. Bousch proved that is locally connected, and Odlyzko and Poonen studied the related set of all complex roots of polynomials with coefficients 0 and 1. We give an algorithm to construct this set and study its geometric structure. In contrast to the Mandelbrot set for quadratic maps, it is shown that is not simply connected.