On the distribution of mantissae in nonautonomous difference equations

References

• Aulbach , B. , Elaydi , S. and Ziegler , K. 2004 . “ Asymptotic solutions of a discrete Schrödinger equation arising from a Dirac equation with random mass ” . In New Progress in Difference Equations , Edited by: Aulbach , B. , Elaydi , S. and Ladas , G. 349 – 358 . London : Taylor and Francis .
   Google Scholar
• Aulbach , B. and Wanner , T. 2003 . Invariant foliations and decoupling of nonautonomous difference equations . Journal of Difference Equations and Applications , 9 : 459 – 472 .
   Web of Science ®Google Scholar
• Benford , F. 1938 . The law of anomalous numbers . Proceedings of the American Philosophical Society , 78 : 551 – 572 .
   Google Scholar
• Berger , A. 2005 . Multi-dimensional dynamical systems and Benford's Law . Discrete Continuous Dynamic Systems , 13 : 219 – 237 .
   Web of Science ®Google Scholar
• Berger , A. 2006 . Benford's Law in power-like dynamical systems . Stochastic Dynamics , 5 : 587 – 607 .
   Web of Science ®Google Scholar
• Berger , A. , Bunimovich , L.A. and Hill , T.P. 2005 . One-dimensional dynamical systems and Benford's Law . Transactions of the American Mathematical Society , 357 : 197 – 219 .
   Web of Science ®Google Scholar
• Berger , A. and Hill , T.P. 2007 . Newton's method obeys Benford's Law . American Mathematical Monthly , 114 : 588 – 601 .
   Web of Science ®Google Scholar
• Brown , J. and Duncan , R. 1970 . Modulo one uniform distribution of the sequence of logarithms of certain recursive sequences . Fibonacci Quarterly , 8 : 482 – 486 .
   Google Scholar
• Dendrinos , D.S. and Sonis , M. 1990 . Chaos and Socio-Spatial Dynamics , New York : Springer .
   Google Scholar
• Diaconis , P. 1979 . The distribution of leading digits and uniform distribution mod 1 . The Annals of Probability , 5 : 72 – 81 .
   Web of Science ®Google Scholar
• Gottwald , G. and Nicol , M. 2001 . On the nature of Benford's Law . Physics A , 303 : 387 – 396 .
   Web of Science ®Google Scholar
• Hill , T.P. 1996 . A statistical derivation of the significant-digit law . Statistical Science , 10 : 354 – 363 .
   Web of Science ®Google Scholar
• Katok , A. and Hasselblatt , B. 1995 . Introduction to the Modern Theory of Dynamical Systems , Cambridge : Cambridge University Press .
   Google Scholar
• Kontorovich , A. and Miller , S. 2005 . Benford's Law, values of L-functions and the 3x+1 problem . Acta Arithmetica , 120 : 269 – 297 .
   Web of Science ®Google Scholar
• Kuipers , L. and Niederreiter , H. 1974 . Uniform Distribution of Sequences , New York : Wiley .
   Google Scholar
• Ley , E. 1996 . On the peculiar distribution of the US stock indices digits . American Statistics , 50 : 311 – 313 .
   Web of Science ®Google Scholar
• Lorenz , H.-W. 1993 . Nonlinear Dynamical Economics and Chaotic Motion , 2nd ed. , Berlin : Springer .
   Google Scholar
• Markus , L. 1956 . Asymptotically autonomous differential systems . Annals of Mathematics Studies , 3 : 17 – 29 .
   Google Scholar
• Miller, S. and Nigrini, M.J., 2006, Order statistics and shifted almost Benford behavior, preprint.
   Google Scholar
• Nigrini , M.J. 2000 . Nigrini, Digital Analysis Using Benford's Law: Tests and Statistics for Auditors , 2nd ed. , Vancouver : Global Audit Publications .
   Google Scholar
• Palmer , K. 2000 . Shadowing in Dynamical Systems , Kluwer : Theory and Applications .
   Google Scholar
• Raimi , R. 1976 . The first digit problem . American Mathematical Monthly , 102 : 322 – 327 .
   Google Scholar
• Snyder , M. , Curry , J. and Dougherty , A. 2001 . Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law . Physical Review E , 64 : 1 – 5 .
   Web of Science ®Google Scholar
• Schatte , P. 1998 . On mantissa distributions in computing and Benford's law . Journal of Information Processing and Cybernetics , 24 : 443 – 455 .
   Google Scholar
• Tolle , C. , Budzien , J. and LaViolette , R. 2000 . Do dynamical systems follow Benford's law? . Chaos , 10 : 331 – 337 .
   PubMed Web of Science ®Google Scholar