Phys. Rev. Lett. 64, 2354–2357 (1990)Unpredictability and undecidability in dynamical systemsReceived 18 August 1989; published in the issue dated 14 May 1990 We show that motion with as few as three degrees of freedom (for instance, a particle moving in a three-dimensional potential) can be equivalent to a Turing machine, and so be capable of universal computation. Such systems possess a type of unpredictability qualitatively stronger than that which has been previously discussed in the study of low-dimensional chaos: Even if the initial conditions are known exactly, virtually any question about their long-term dynamics is undecidable. © 1990 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.64.2354
DOI:
10.1103/PhysRevLett.64.2354
PACS:
05.45.+b, 02.50.+s, 05.40.+j
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