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Volumn 17, Issue 2, 2011, Pages 137-159

Some dynamical properties of Benford sequences

Author keywords

Benford sequence; Benford's law; Non autonomous dynamical system; Shadowing; Uniform distribution mod 1

Indexed keywords


EID: 79952966391     PISSN: 10236198     EISSN: 15635120     Source Type: Journal    
DOI: 10.1080/10236198.2010.549012     Document Type: Article
Times cited : (2)

References (28)
  • 1
    • 0000956831 scopus 로고
    • The law of anomalous numbers
    • F. Benford, The law of anomalous numbers, Proc. Amer. Philos. Soc. 78 (1938), pp. 551-572.
    • (1938) Proc. Amer. Philos. Soc. , vol.78 , pp. 551-572
    • Benford, F.1
  • 2
    • 2942661294 scopus 로고    scopus 로고
    • de Gruyter, Berlin, New York
    • A. Berger, Chaos and Chance, de Gruyter, Berlin, New York, 2001.
    • (2001) Chaos and Chance
    • Berger, A.1
  • 3
    • 18144422787 scopus 로고    scopus 로고
    • Multi-dimensional dynamical systems and Benford's Law
    • A. Berger, Multi-dimensional dynamical systems and Benford's Law, Discr. Contin. Dyn. Syst. 13 (2005), pp. 219-237.
    • (2005) Discr. Contin. Dyn. Syst. , vol.13 , pp. 219-237
    • Berger, A.1
  • 4
    • 33746310018 scopus 로고    scopus 로고
    • Benford's Law in power-like dynamical systems
    • A. Berger, Benford's Law in power-like dynamical systems, Stoch. Dyn. 5 (2006), pp. 587-607.
    • (2006) Stoch. Dyn. , vol.5 , pp. 587-607
    • Berger, A.1
  • 5
    • 34547206747 scopus 로고    scopus 로고
    • Newton's method obeys Benford's Law
    • A. Berger and T.P. Hill, Newton's method obeys Benford's Law, Amer. Math. Monthly 114 (2007), pp. 588-601.
    • (2007) Amer. Math. Monthly , vol.114 , pp. 588-601
    • Berger, A.1    Hill, T.P.2
  • 7
    • 34547220090 scopus 로고    scopus 로고
    • On the distribution of mantissae in nonautonomous difference equations
    • A. Berger and S. Siegmund, On the distribution of mantissae in nonautonomous difference equations, J. Difference Equ. Appl. 13 (2007), pp. 829-845.
    • (2007) J. Difference Equ. Appl. , vol.13 , pp. 829-845
    • Berger, A.1    Siegmund, S.2
  • 8
    • 12744263576 scopus 로고    scopus 로고
    • One-dimensional dynamical systems and Benford's law
    • A. Berger, L.A. Bunimovich, and T.P. Hill, One-dimensional dynamical systems and Benford's law, Trans. Amer. Math. Soc. 357 (2005), pp. 197-219.
    • (2005) Trans. Amer. Math. Soc. , vol.357 , pp. 197-219
    • Berger, A.1    Bunimovich, L.A.2    Hill, T.P.3
  • 10
    • 12744275247 scopus 로고
    • Modulo one uniform distribution of the sequence of logarithms of certain recursive sequences
    • J. Brown and R. Duncan, Modulo one uniform distribution of the sequence of logarithms of certain recursive sequences, Fibonacci Quart. 8 (1970), pp. 482-486.
    • (1970) Fibonacci Quart. , vol.8 , pp. 482-486
    • Brown, J.1    Duncan, R.2
  • 11
    • 0002417821 scopus 로고
    • The distribution of leading digits and uniform distribution mod 1
    • P. Diaconis, The distribution of leading digits and uniform distribution mod 1, Ann. Probab. 5 (1979), pp. 72-81.
    • (1979) Ann. Probab. , vol.5 , pp. 72-81
    • Diaconis, P.1
  • 12
    • 0037081064 scopus 로고    scopus 로고
    • On the nature of Benford's Law
    • G. Gottwald and M. Nicol, On the nature of Benford's Law, Phys. A 303 (2001), pp. 387-396.
    • (2001) Phys. A , vol.303 , pp. 387-396
    • Gottwald, G.1    Nicol, M.2
  • 13
    • 84966250122 scopus 로고
    • Base-invariance implies Benford's Law
    • T.P. Hill, Base-invariance implies Benford's Law, Proc. Amer. Math. Soc. 123 (1995), pp. 887-895.
    • (1995) Proc. Amer. Math. Soc. , vol.123 , pp. 887-895
    • Hill, T.P.1
  • 14
    • 84972541029 scopus 로고    scopus 로고
    • A statistical derivation of the significant-digit law
    • T.P. Hill, A statistical derivation of the significant-digit law, Stat. Sci. 10 (1996), pp. 354-363.
    • (1996) Stat. Sci. , vol.10 , pp. 354-363
    • Hill, T.P.1
  • 16
    • 33645139599 scopus 로고    scopus 로고
    • Benford's law, values of L-functions and the 3x{thorn}1 problem
    • A. Kontorovich and S. Miller, Benford's law, values of L-functions and the 3x{thorn}1 problem, Acta Arithmet. 120 (2005), pp. 269-297.
    • (2005) Acta Arithmet. , vol.120 , pp. 269-297
    • Kontorovich, A.1    Miller, S.2
  • 18
    • 0030328721 scopus 로고    scopus 로고
    • On the peculiar distribution of the US stock indices digits
    • E. Ley, On the peculiar distribution of the US stock indices digits, Amer. Stat. 50 (1996), pp. 311-313.
    • (1996) Amer. Stat. , vol.50 , pp. 311-313
    • Ley, E.1
  • 20
    • 0003038640 scopus 로고
    • Note on the frequency of use of the different digits in natural numbers
    • S. Newcomb, Note on the frequency of use of the different digits in natural numbers, Amer. J. Math. 4 (1881), pp. 39-40.
    • (1881) Amer. J. Math. , vol.4 , pp. 39-40
    • Newcomb, S.1
  • 21
  • 22
    • 0001779250 scopus 로고
    • Almost sure invariance principles for partial sums of weakly dependent random variables
    • W. Philipp and W.F. Stout, Almost sure invariance principles for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc. 161 (1975).
    • (1975) Mem. Amer. Math. Soc. , vol.161
    • Philipp, W.1    Stout, W.F.2
  • 23
    • 0037611243 scopus 로고
    • The first digit problem
    • R. Raimi, The first digit problem, Amer. Math. Monthly 102 (1976), pp. 322-327.
    • (1976) Amer. Math. Monthly , vol.102 , pp. 322-327
    • Raimi, R.1
  • 24
    • 0039340359 scopus 로고
    • On H∞-summability and the uniform distribution of sequences
    • P. Schatte, On H∞-summability and the uniform distribution of sequences, Math. Nachr. 113 (1983), pp. 237-243.
    • (1983) Math. Nachr. , vol.113 , pp. 237-243
    • Schatte, P.1
  • 25
    • 0010075497 scopus 로고    scopus 로고
    • On mantissa distributions in computing and Benford's law
    • P. Schatte, On mantissa distributions in computing and Benford's law, J. Inform. Process. Cybern. 24 (1998), pp. 443-455.
    • (1998) J. Inform. Process. Cybern. , vol.24 , pp. 443-455
    • Schatte, P.1
  • 26
    • 0035418924 scopus 로고    scopus 로고
    • Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law
    • M. Snyder, J. Curry, and A. Dougherty, Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law, Phys. Rev. E 64 (2001), pp. 1-5.
    • (2001) Phys. Rev. E , vol.64 , pp. 1-5
    • Snyder, M.1    Curry, J.2    Dougherty, A.3
  • 27
    • 0034195340 scopus 로고    scopus 로고
    • Do dynamical systems follow Benford's law?
    • C. Tolle, J. Budzien, and R. LaViolette, Do dynamical systems follow Benford's law?, Chaos 10 (2000), pp. 331-337.
    • (2000) Chaos , vol.10 , pp. 331-337
    • Tolle, C.1    Budzien, J.2    la Violette, R.3
  • 28
    • 17644434420 scopus 로고    scopus 로고
    • S-unimodal Misiurewicz maps with flat critical points
    • R. Zweimüller, S-unimodal Misiurewicz maps with flat critical points, Fund. Math. 181 (2004), pp. 1-25.
    • (2004) Fund. Math. , vol.181 , pp. 1-25
    • Zweimüller, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.