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Volumn 131, Issue 3, 1998, Pages 225-251

Lq-spectrum of the Bernoulli convolution associated with the golden ratio

Author keywords

Bernoulli convolution; Golden ratio; Hausdorff dimension; Lq dimension; Lq spectrum; Multifractal measure; Renewal equation; Self similarity

Indexed keywords


EID: 0001095597     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (56)

References (33)
  • 2
    • 33646893145 scopus 로고
    • The entropy of a certain infinitely convolved Bernoulli measure
    • J. C. Alexander and D. Zagier, The entropy of a certain infinitely convolved Bernoulli measure, J. London Math. Soc. 44 (1991), 121-134.
    • (1991) J. London Math. Soc. , vol.44 , pp. 121-134
    • Alexander, J.C.1    Zagier, D.2
  • 3
    • 44049118235 scopus 로고
    • Multifractal decompositions of Moran fractals
    • R. Cawley and R. D. Mauldin, Multifractal decompositions of Moran fractals, Adv. Math. 92 (1992), 196-236.
    • (1992) Adv. Math. , vol.92 , pp. 196-236
    • Cawley, R.1    Mauldin, R.D.2
  • 4
    • 0001141522 scopus 로고
    • The dimension spectrum of some dynamical systems
    • P. Collet, J. L. Lebowitz and A. Porzio, The dimension spectrum of some dynamical systems, J. Statist. Phys. 47 (1987), 609-644.
    • (1987) J. Statist. Phys. , vol.47 , pp. 609-644
    • Collet, P.1    Lebowitz, J.L.2    Porzio, A.3
  • 5
    • 0001586785 scopus 로고
    • On the thermodynamic formalism for multifractal functions
    • I. Daubechies and J. Lagarias, On the thermodynamic formalism for multifractal functions, Rev. Math. Phys. 6 (1994), 1033-1070.
    • (1994) Rev. Math. Phys. , vol.6 , pp. 1033-1070
    • Daubechies, I.1    Lagarias, J.2
  • 6
    • 84962991716 scopus 로고
    • Multifractal decompositions of digraph recursive fractals
    • G. A. Edgar and R. D. Mauldin, Multifractal decompositions of digraph recursive fractals, Proc. London Math. Soc. 65 (1992), 604-628.
    • (1992) Proc. London Math. Soc. , vol.65 , pp. 604-628
    • Edgar, G.A.1    Mauldin, R.D.2
  • 7
    • 0001126766 scopus 로고
    • On a family of symmetric bernoulli convolutions
    • P. Erdos, On a family of symmetric Bernoulli convolutions, Amer. J. Math. 61 (1939), 974-976.
    • (1939) Amer. J. Math. , vol.61 , pp. 974-976
    • Erdos, P.1
  • 10
    • 0001816154 scopus 로고
    • On the singularity structure of fully developed turbulence
    • North-Holland, Amsterdam
    • U. Frisch and G. Parisi, On the singularity structure of fully developed turbulence, in: Proc. Internat. School Phys., "Enrico Fermi" Course LXXXVIII, North-Holland, Amsterdam, 1985, 84-88.
    • (1985) Proc. Internat. School Phys., "Enrico Fermi" Course , vol.88 , pp. 84-88
    • Frisch, U.1    Parisi, G.2
  • 11
    • 84972575493 scopus 로고
    • Entropy and singularity of infinite convolutions
    • A. M. Garsia, Entropy and singularity of infinite convolutions, Pacific J. Math. 13 (1963), 1159-1169.
    • (1963) Pacific J. Math. , vol.13 , pp. 1159-1169
    • Garsia, A.M.1
  • 12
    • 3342916075 scopus 로고
    • Fractal measures and their singularities: The characterization of strange sets
    • T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Fractal measures and their singularities: The characterization of strange sets, Phys. Rev. A 33 (1986), 1141-1151.
    • (1986) Phys. Rev. A , vol.33 , pp. 1141-1151
    • Halsey, T.C.1    Jensen, M.H.2    Kadanoff, L.P.3    Procaccia, I.4    Shraiman, B.I.5
  • 13
    • 21744461099 scopus 로고    scopus 로고
    • The local dimensions of the bernoulli convolution associated with the golden number
    • T. Y. Hu, The local dimensions of the Bernoulli convolution associated with the golden number, Trans. Amer. Math. Soc. 349 (1997), 2917-2940.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 2917-2940
    • Hu, T.Y.1
  • 14
    • 0001265433 scopus 로고
    • Fractals and self-similarity
    • J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), 713-747.
    • (1981) Indiana Univ. Math. J. , vol.30 , pp. 713-747
    • Hutchinson, J.E.1
  • 15
    • 0032105005 scopus 로고    scopus 로고
    • Random series in powers of algebraic integers: Hausdorff dimension of the limit distribution
    • to appear
    • S. P. Lalley, Random series in powers of algebraic integers: Hausdorff dimension of the limit distribution, J. London Math. Soc., to appear.
    • J. London Math. Soc.
    • Lalley, S.P.1
  • 16
    • 0000815707 scopus 로고
    • Fractal measures and mean p-variations
    • K.-S. Lau, Fractal measures and mean p-variations, J. Funct. Anal. 108 (1992), 427-457.
    • (1992) J. Funct. Anal. , vol.108 , pp. 427-457
    • Lau, K.-S.1
  • 17
    • 38248998558 scopus 로고
    • Dimension of a family of singular Bernoulli convolutions
    • _, Dimension of a family of singular Bernoulli convolutions, ibid. 116 (1993), 335-358.
    • (1993) J. Funct. Anal. , vol.116 , pp. 335-358
  • 18
    • 0033555068 scopus 로고    scopus 로고
    • Multifractal measures and a weak separation condition
    • to appear
    • K.-S. Lau and S.-M. Ngai, Multifractal measures and a weak separation condition, Adv. Math., to appear.
    • Adv. Math.
    • Lau, K.-S.1    Ngai, S.-M.2
  • 20
    • 0002706785 scopus 로고
    • Mean quadratic variations and Fourier asymptotics of self-similar measures
    • K.-S. Lau and J. Wang, Mean quadratic variations and Fourier asymptotics of self-similar measures, Monatsh. Math. 115 (1993), 99-132.
    • (1993) Monatsh. Math. , vol.115 , pp. 99-132
    • Lau, K.-S.1    Wang, J.2
  • 21
    • 0001707212 scopus 로고
    • A dimension formula for Bernoulli convolution
    • F. Ledrappier and A. Porzio, A dimension formula for Bernoulli convolution, J. Statist. Phys. 76 (1994), 1307-1327.
    • (1994) J. Statist. Phys. , vol.76 , pp. 1307-1327
    • Ledrappier, F.1    Porzio, A.2
  • 22
    • 0008998845 scopus 로고
    • The dimension spectrum of the maximal measure
    • A. O. Lopes, The dimension spectrum of the maximal measure, SIAM J. Math. Anal. 20 (1989), 1243-1254.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 1243-1254
    • Lopes, A.O.1
  • 23
    • 21944433331 scopus 로고    scopus 로고
    • q-spectrum of a measure
    • q-spectrum of a measure, Proc. Amer. Math. Soc. 125 (1997), 2943-2951.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 2943-2951
    • Ngai, S.-M.1
  • 24
    • 85027614017 scopus 로고
    • A multifractal formalism
    • L. Olsen, A multifractal formalism, Adv. Math. 116 (1995), 82-195.
    • (1995) Adv. Math. , vol.116 , pp. 82-195
    • Olsen, L.1
  • 25
    • 0000690674 scopus 로고
    • On the Hausdorff dimension of some fractal sets
    • F. Przytycki and M. Urbański, On the Hausdorff dimension of some fractal sets, Studia Math. 93 (1989), 155-186.
    • (1989) Studia Math. , vol.93 , pp. 155-186
    • Przytycki, F.1    Urbański, M.2
  • 26
    • 84974252535 scopus 로고
    • The singularity spectrum f(α) for cookie-cutters
    • D. Rand, The singularity spectrum f(α) for cookie-cutters, Ergodic Theory Dynam. Systems 9 (1989), 527-541.
    • (1989) Ergodic Theory Dynam. Systems , vol.9 , pp. 527-541
    • Rand, D.1
  • 28
    • 58149362177 scopus 로고
    • An improved multifractal formalism and self-similar measures
    • R. Riedi, An improved multifractal formalism and self-similar measures, J. Math. Anal. Appl. 189 (1995), 462-490.
    • (1995) J. Math. Anal. Appl. , vol.189 , pp. 462-490
    • Riedi, R.1
  • 31
    • 0000660967 scopus 로고
    • n (an Erdos problem)
    • n (an Erdos problem), Ann. of Math. 142 (1995), 611-625.
    • (1995) Ann. of Math. , vol.142 , pp. 611-625
    • Solomyak, B.1
  • 32
    • 0000493711 scopus 로고
    • Self-similar measures and their Fourier transforms III
    • R. S. Strichartz, Self-similar measures and their Fourier transforms III, Indiana Univ. Math. J. 42 (1993), 367-411.
    • (1993) Indiana Univ. Math. J. , vol.42 , pp. 367-411
    • Strichartz, R.S.1
  • 33
    • 21344474424 scopus 로고
    • Densities of self-similar measures on the line
    • R. S. Strichartz, A. Taylor and T. Zhang, Densities of self-similar measures on the line, Experiment. Math. 4 (1995), 101-128.
    • (1995) Experiment. Math. , vol.4 , pp. 101-128
    • Strichartz, R.S.1    Taylor, A.2    Zhang, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.