Parker, Matthew W. (2003) Undecidability in Rn: Riddled Basins, the KAM Tori, and the Stability of the Solar System. Philosophy of Science, 70 (2). pp. 359-382.
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Abstract
Some have suggested that certain classical physical systems have undecidable long-term behavior, without specifying an appropriate notion of decidability over the reals. We introduce such a notion, decidability in μ (or d-μ) for any measure μ, which is particularly appropriate for physics and in some ways more intuitive than Ko’s (1991) recursive approximability (r.a.). For Lebesgue measure λ, d-λ implies r.a. Sets with positive λ-measure that are sufficiently “riddled” with holes are never d-λ but are often r.a. This explicates Sommerer and Ott’s (1996) claim of uncomputable behavior in a system with riddled basins of attraction. Furthermore, it clarifies speculations that the stability of the solar system (and similar systems) may be undecidable, for the invariant tori established by KAM theory form sets that are not d-λ.
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| Item Type: | Published Article or Volume | ||||||
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| Keywords: | Decidable, stability, chaos, KAM, Ko, riddled basin, real numbers, continuous space, computable, planetary system, nearly integrable, n-body problem, 3-body problem, dynamical systems, computable analysis | ||||||
| Subjects: | Specific Sciences > Computation/Information > Classical Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Classical Physics Specific Sciences > Computation/Information Specific Sciences > Computer Science |
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| Depositing User: | Dr. Matthew Parker | ||||||
| Date Deposited: | 03 Jul 2017 14:35 | ||||||
| Last Modified: | 03 Jul 2017 14:35 | ||||||
| Item ID: | 13175 | ||||||
| Journal or Publication Title: | Philosophy of Science | ||||||
| Publisher: | University of Chicago Press | ||||||
| Official URL: | http://www.journals.uchicago.edu/doi/abs/10.1086/3... | ||||||
| DOI or Unique Handle: | https://doi.org/10.1086/375472 | ||||||
| Subjects: | Specific Sciences > Computation/Information > Classical Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Classical Physics Specific Sciences > Computation/Information Specific Sciences > Computer Science |
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| Date: | 1 April 2003 | ||||||
| Page Range: | pp. 359-382 | ||||||
| Volume: | 70 | ||||||
| Number: | 2 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/13175 |
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