Origami, affine maps, and complex dynamics

Abstract

We investigate the combinatorial and dynamical properties of so-called nearly Euclidean Thurston maps, or NET maps. These maps are perturbations of many-to-one folding maps of an affine two-sphere to itself. The close relationship between NET maps and affine maps makes computation of many invariants tractable. In addition to this, NET maps are quite diverse, exhibiting many different behaviors. We discuss data, findings, and new phenomena.

Cited by in corpus (3)

• Eliminating Thurston obstructions and controlling dynamics on curves
• Quadratic matings and ray connections
• On the rank of the Thurston pullback map