arXiv subjects

A. Gonzalez Gomez

Publications and source records attributed to A. Gonzalez Gomez.

2 recordsLinked to original sources

arXiv2009

Composition law of cardinal order permutations

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.

nlin.CD↗

arXiv2008

The Universal Cardinal Ordering of Fixed Points

We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a corollary. The problem present in the symbolic sequences is solved. There, repeated symbols appear, for example, the R (right), which cannot be distinguished among them as it is not known which R is the rightmost of them all. Therefore, there is a lack of information about the dynamical system. Interestingly enough, it is important to point that this theorem needs no previous information about any other orbit.

nlin.CD↗