The Dynamics of Twisted Tent Maps

Abstract

This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The action of this map can be visualized as the complex scaling of the plane followed by folding the plane once. Most of the time, scaling by a complex number will "twist" the plane, hence the name. The "folding" both breaks analyticity (and even smoothness) and leads to interesting dynamics ranging from easily understood and highly geometric behavior to chaotic behavior and fractals.