Spread polynomials, rotations and the butterfly effect
Classical Analysis and ODEs
2009-11-06 v1 Algebraic Topology
Abstract
The spread between two lines in rational trigonometry replaces the concept of angle, allowing the complete specification of many geometrical and dynamical situations which have traditionally been viewed approximately. This paper investigates the case of powers of a rational spread rotation, and in particular, a curious periodicity in the prime power decomposition of the associated values of the spread polynomials, which are the analogs in rational trigonometry of the Chebyshev polynomials of the first kind. Rational trigonometry over finite fields plays a role, together with non-Euclidean geometries.
Cite
@article{arxiv.0911.1025,
title = {Spread polynomials, rotations and the butterfly effect},
author = {Shuxiang Goh and N. J. Wildberger},
journal= {arXiv preprint arXiv:0911.1025},
year = {2009}
}
Comments
14 pages, 3 figures