ar X iv : c ha o - dy n / 98 12 01 6 v 1 9 D ec 1 99 8 Queues , Stacks , and Transcendentality at the Transition to Chaos
نویسنده
چکیده
We examine the one-humped map at the period-doubling transition to chaos, and ask whether its long-term memory is stack-like (last-in, first-out) or queue-like (first-in, first-out). We show that it can be recognized by a real-time automaton with one queue, or two stacks, and give several new grammatical characterizations of it. We argue that its memory has a queue-like character, since a single stack does not suffice. We also show that its dynamical zeta function, generating function and growth function are transcendental. The same results hold for any periodmultiplying cascade. We suggest that transcendentality might be a sign of dynamical phase transitions in other systems as well.
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