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.Comment: 87 pages. This is my Ph.D. thesis from IUPU
