Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2008-03-06
Nonlinear Sciences
Chaotic Dynamics
19 pages, 4 figures
Scientific paper
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.
Gomez Gonzalez A.
Martin Jesus San
Moscoso Jose M.
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