On the Mandelbrot set for pairs of linear maps

Abstract

A Mandelbrot set ℳ for pairs of complexlinear maps was introduced by Barnsley and Harringtonin 1985. Bousch proved that ℳ is locallyconnected, and Odlyzko and Poonen studied the related setof 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 Mandelbrotset for quadratic maps, it is shown that ℳ is not simply connected.