Origami, affine maps, and complex dynamics

Authors

William Floyd, Virginia Polytechnic Institute and State University
Gregory Kelsey, Bellarmine University
Sarah Koch, University of Michigan, Ann Arbor
Russell Lodge, Institute for Mathematical Sciences
Walter Parry, Eastern Michigan University
Kevin M. Pilgrim, Indiana University Bloomington
Edgar Saenz, Virginia Polytechnic Institute and State University

Document Type

Article

Publication Date

2017

Department/School

Mathematics

Publication Title

Arnold Mathematical Journal

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.

Link to Published Version

DOI: 10.1007/s40598-017-0071-0

Recommended Citation

Floyd, W., Kelsey, G., Koch, S., Lodge, R., Parry, W., Pilgrim, K. M., & Saenz, E. (2017). Origami, affine maps, and complex dynamics. Arnold Mathematical Journal, 3(3), 365–395. https://doi.org/10.1007/s40598-017-0071-0