Do dynamical systems follow Benford's law?

Chaos

Volumn 10, Issue 2, 2000, Pages 331-336

  Tolle, Charles R ^a   Budzien, Joanne L ^a   LaViolette, Randall A ^a  

^a IDAHO NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034195340     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166498     Document Type: Article

References (24)

1. S. Newcomb, "Note on the frequency of use of the different digits in natural numbers," Am. J. Math. 4, 39-40 (1881).
2. F. Benford, "The law of anomalous numbers," Proc. Am. Philos. Soc. 78, 551-572 (1938).
3. R. A. Raimi, "The first digit problem," Am. Math. Monthly 83, 521-538 (1976).
4. T. P. Hill, "Base-invariance implies Benford's law," Proc. Am. Math. Soc. 123, 887-895 (1995).
5. T. P. Hill, "The significant-digit phenomenon," Am. Math. Monthly 102, 322-326 (1995).
6. T. P. Hill, "A statistical derivation of the significant-digit law," Stat. Sci. 10, 354-363 (1995).
7. R. A. Raimi, "The peculiar distribution of first digits," Sci. Am. 221, 109-119 (1969).
8. T. P. Hill, "The first digit phenomenon," Am. Sci. 86, 358-363 (1998).
9. R. Matthews, "The power of one," New Sci. 163:2194, 27-30 (1999); see also http://www.newscientist.com/ns/19990710/thepowerof.html
10. E. W. Weisstein, http://www.treasuretroves.com/math/BenfordsLaw. html, 11 August 1999.
11. J. V. Bradley, Distribution-Free Statistical Tests (Prentice-Hall, Englewood Cliffs, NJ, 1968).
12. D. Kaplan and L. Glass, Understanding Nonlinear Dynamics (Springer-Verlag, New York, 1995).
13. S. Wolfram, Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).
14. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press. Oxford, 1987).
15. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, 2nd ed. (Academic, San Diego, 1986).
16. A. K. Rappe, C. J. Casewit, K. S. Colwell, W. A. Goddard, and W. M. Skiff, "UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations," J. Am. Chem. Soc. 114, 10024-10046 (1992).
17. H. J. C. Berendsen, J. P. C. Postma, W. F. van Gunsteren, A. Di Nola, and J. R. Haak, "Molecular dynamics with coupling to an external bath," J. Chem. Phys. 81, 3684-3689 (1984).
18. M. J. L. Sangster and M. Dixon, "Interionic potentials in alkali halides and their use in simulation of molten salts," Adv. Phys. 25, 247-342 (1976).
19. F. H. Stillinger and T. A. Weber, "Packing structures and transitions in liquids and solids," Science 225, 983-989 (1984).
20. F. H. Stillinger and R. A. LaViolette, "Sensitivity of liquid-state inherent structure to details of intermolecular forces," J. Chem. Phys. 83, 6413 (1985).
21. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Addison-Wesley, Reading, PA, 1994).
22. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, "Testing for nonlinearly in time series: the method of surrogate data," Physica D 58, 77-94 (1992).
23. S. Wolfram, "Random sequence generation by cellular automata," Adv. Appl. Math. 7, 123-169 (1986).
24. M. Nigrini, "A taxpayer compliance application of Benford's law," J. Amer. Tax. Assoc. 18, 72-91 (1996).