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From Symbolic Dynamics to a Digital Approach

We show that the numbers generated by the symbolic dynamics of Feigenbaum attractors are transcendental. Due to the asymmetry of the chaotic attractors of unimodal maps around the maximum in the general case, a standard conjecture, that the occurrence of chaos is related to the transcendence of the number defined by the corresponding symbolic dynamics is reassessed and formulated in a quantitative manner. It is concluded that transcendence may provide an appropriate measure of complexity.