Composition law of cardinal order permutations

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 $s-$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.

References in corpus (3)

• The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems
• Forbidden ordinal patterns in higher dimensional dynamics
• The Universal Cardinal Ordering of Fixed Points