Composition law of cardinal order permutations
Chaotic Dynamics
2015-05-13 v1
Abstract
In this paper the theorems that determine composition laws for both cardinal ordering permutations and their inverses are proven. So, the relative positions of points in a hs-periodic orbit become completely known as well as in which order those points are visited. No matter how a hs-periodic orbit emerges, be it through a period doubling cascade (s=2^n) of the h-periodic orbit, or as a primary window (like the saddle-node bifurcation cascade with h=2^n), or as a secondary window (the birth of a periodic window inside the h-periodic one). Certainly, period doubling cascade orbits are particular cases with h=2 and s=2^n. Both composition laws are also shown in algorithmic way for their easy use.
Cite
@article{arxiv.0908.0065,
title = {Composition law of cardinal order permutations},
author = {Jesus San Martin and Ma. Jose Moscoso and A. Gonzalez Gomez},
journal= {arXiv preprint arXiv:0908.0065},
year = {2015}
}