The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
Unpredictability and undecidability in dynamical systems
Abstract
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.
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Citations
Cites
Computation: Finite and Infinite Machines.
Clarke, D. A., & Minsky, M. L. (1968) · The American Mathematical Monthly · doi:10.2307/2313471 · Cited by 2,583
Theory of Recursive Functions and Effective Computability
Cooper, D. C. (1969) · The Computer Journal · doi:10.1093/comjnl/12.1.28 · Cited by 2,539
Differentiable Dynamical Systems
Smale, S. (1980) · The Mathematics of Time · doi:10.1007/978-1-4613-8101-3_1 · Cited by 2,478
Fredkin, E., & Toffoli, T. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf01857727 · Cited by 1,896
Computation theory of cellular automata
Wolfram, S. (1984) · Communications in Mathematical Physics · doi:10.1007/bf01217347 · Cited by 625
Differential and Combinatorial Topology: A Symposium in Honor of Marston Morse
Cairns, S. S. (1965) · Princeton University Press eBooks · doi:10.1515/9781400874842 · Cited by 282
Undecidability and intractability in theoretical physics
Wolfram, S. (1985) · Physical Review Letters · doi:10.1103/physrevlett.54.735 · Cited by 238
Cited by
A survey of computational complexity results in systems and control
Blondel, V. D., & Tsitsiklis, J. N. (2000) · Automatica · doi:10.1016/s0005-1098(00)00050-9 · Cited by 732
Computational Mechanics: Pattern and Prediction, Structure and Simplicity
Shalizi, C. R., & Crutchfield, J. P. (2001) · Journal of Statistical Physics · doi:10.1023/a:1010388907793 · Cited by 471
Quantum automata and quantum grammars
Moore, C., & Crutchfield, J. P. (2000) · Theoretical Computer Science · doi:10.1016/s0304-3975(98)00191-1 · Cited by 406
Self-citationDynamic link of memory—Chaotic memory map in nonequilibrium neural networks
Tsuda, I. (1992) · Neural Networks · doi:10.1016/s0893-6080(05)80029-2 · Cited by 353
Moore, C., & Mertens, S. (2011) · doi:10.1093/acprof:oso/9780199233212.001.0001 · Cited by 347
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Metadata
- Authors
- Moore, C.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1990-05-14
- Volume
- 64
- Issue
- 20
- Pages
- 2354-2357
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2065597356
- Cited by
- 414
- References
- 7
- FWCI
- 11.01
- Type
- journal article
- Language
- en
- Open access
- closed
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- Moore, C. (1990). Unpredictability and undecidability in dynamical systems. Physical Review Letters. https://doi.org/10.1103/physrevlett.64.2354
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