Regularity in nonlinear dynamical systems


Abstract
Laws of nature have been traditionally thought to express regularities in the systems which they describe, and, via their expression of regularities, to allow us to explain and predict the behavior of these systems. Using the driven simple pendulum as a paradigm, we identify three senses that regularity might have in connection with nonlinear dynamical systems: periodicity, uniqueness, and perturbative stability. Such systems are always regular only in the second of these senses, and that sense is not robust enough to support predictions. We thus illustrate precisely how physical laws in the classical regime of dynamical systems fail to exhibit predictive power. *R. G. Holt gratefully acknowledges the support of the National Center for Physical Acoustics at Oxford, Mississippi, and the Office of Naval Research.
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DOI 10.1093/bjps/44.4.711
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Philosophy of Natural Science.Carl G. Hempel - 1966 - Englewood Cliffs, N.J., Prentice-Hall.
Laws of Nature.Fred Dretske - 1977 - Philosophy of Science 44 (2):248-268.
Philosophy of Natural Science.Carl G. Hempel - 1967 - British Journal for the Philosophy of Science 18 (1):70-72.

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Stability in Cosmology, From Einstein to Inflation.C. D. McCoy - forthcoming - In Claus Beisbart, Tilman Sauer & Christian Wüthrich (eds.), Thinking About Space and Time. Basel: Birkhäuser.

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