William Floyd, Gregory Kelsey, Sarah Koch, Russell Lodge, Walter Parry, Kevin M. Pilgrim, Edgar Saenz
Published 2016-12-19Version 1
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.
Complex Dynamics of the Difference Equation $\displaystyle z_{n+1}=\fracĪ±{z_{n}}+ \fracĪ²{z_{n-1}}$
Modular groups, Hurwitz classes and dynamic portraits of NET maps
Rationality is decidable for nearly Euclidean Thurston maps
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