Self-similarity of Jankins-Neumann ziggurat
Dynamical Systems
2015-03-12 v1
Abstract
Primarily having emerged from a topological question, Jankins-Neumann ziggurat also appears in the theory of dynamical systems on the circle. It describes an answer to the following question: given the rotation numbers of two orientation-preserving circle homeomorphisms, what can be said about the rotation number of their composition? In this paper, we consider a formula, proved by Calegari and Walker, as definition of ziggurat. Using it, we establish its self-similarity. Also, we propose a short proof of equivalence between Calegary-Walker and Jankins-Neumann's descriptions of the ziggurat.
Keywords
Cite
@article{arxiv.1503.03114,
title = {Self-similarity of Jankins-Neumann ziggurat},
author = {Anna Gordenko},
journal= {arXiv preprint arXiv:1503.03114},
year = {2015}
}