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Volumn 183, Issue 1, 1998, Pages 143-199

Self-affine multifractal sierpinski sponges in ℝd

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EID: 0000126935     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1998.183.143     Document Type: Article
Times cited : (100)

References (36)
  • 3
    • 44049118235 scopus 로고
    • Multifractal decomposition of moran fractals
    • R. Cawley and R.D. Mauldin, Multifractal decomposition of Moran fractals, Advances in Mathematics, 92 (1992), 196-236.
    • (1992) Advances in Mathematics , vol.92 , pp. 196-236
    • Cawley, R.1    Mauldin, R.D.2
  • 4
    • 0001743732 scopus 로고
    • Some results on the behavior and estimation of the fractal dimensions of distributions on attractors
    • C.D. Cutler, Some results on the behavior and estimation of the fractal dimensions of distributions on attractors, Journal of Statistical Physics, 62 (1991), 651-708.
    • (1991) Journal of Statistical Physics , vol.62 , pp. 651-708
    • Cutler, C.D.1
  • 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
    • 84976003309 scopus 로고
    • The hausdorff dimension of self-affine fractals
    • K.J. Falconer, The Hausdorff dimension of self-affine fractals, Math. Proc. Camb. Phil. Soc., 103 (1988), 339-350.
    • (1988) Math. Proc. Camb. Phil. Soc. , vol.103 , pp. 339-350
    • Falconer, K.J.1
  • 9
    • 84974200301 scopus 로고
    • The dimension of self-affine fractals II
    • _, The dimension of self-affine fractals II, Math. Proc. Camb. Phil. Soc., 111 (1992), 169-179.
    • (1992) Math. Proc. Camb. Phil. Soc. , vol.111 , pp. 169-179
  • 10
    • 7944232130 scopus 로고
    • The multifractal spectrum of statistically self-similar measures
    • _, The multifractal spectrum of statistically self-similar measures, Journal of Theoretical Probability, 7 (1994), 681-702.
    • (1994) Journal of Theoretical Probability , vol.7 , pp. 681-702
  • 11
    • 0010990456 scopus 로고
    • An exact formula for the measure dimension associated with a class of piecewise linear maps
    • J.S. Geronimo and D. Hardin, An exact formula for the measure dimension associated with a class of piecewise linear maps, Constr. Approx., 5 (1989), 89-98.
    • (1989) Constr. Approx. , vol.5 , pp. 89-98
    • Geronimo, J.S.1    Hardin, D.2
  • 12
    • 33646981873 scopus 로고
    • Characterization of strange attractors
    • P. Grassberger and I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett., 50 (1983), 346-349.
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 346-349
    • Grassberger, P.1    Procaccia, I.2
  • 13
    • 0039200450 scopus 로고
    • A survey of the dimensions of measures
    • Warnemünde, Germany, August
    • H. Haase, A survey of the dimensions of measures, Proceedings of the conference 'Topology and Measure VI', Warnemünde, Germany, August 1991 (eds. C. Bandt, J. Flachsmeyer and H. Haase), in Mathematical Research, 66, 66-75, Topology, Measures, and Fractals, Akademie Verlag, 1992.
    • (1991) Proceedings of the Conference 'Topology and Measure VI , vol.6
    • Haase, H.1
  • 14
    • 0040384965 scopus 로고
    • Topology, Measures, and Fractals, Akademie Verlag
    • H. Haase, A survey of the dimensions of measures, Proceedings of the conference 'Topology and Measure VI', Warnemünde, Germany, August 1991 (eds. C. Bandt, J. Flachsmeyer and H. Haase), in Mathematical Research, 66, 66-75, Topology, Measures, and Fractals, Akademie Verlag, 1992.
    • (1992) Mathematical Research , vol.66 , pp. 66-75
    • Bandt, C.1    Flachsmeyer, J.2    Haase, H.3
  • 15
    • 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.J. 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.J.5
  • 16
    • 0346372923 scopus 로고
    • The infinite number of generalized dimensions of fractals and strange attractors
    • H. Hentschel and I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors, Physica, 8D (1983), 435-444.
    • (1983) Physica , vol.8 D , pp. 435-444
    • Hentschel, H.1    Procaccia, I.2
  • 17
    • 0001265433 scopus 로고
    • Fractals and self-similarity
    • J. 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.1
  • 18
    • 0030530020 scopus 로고    scopus 로고
    • Measures of full dimension on affine-invariant sets
    • R. Kenyon and Y. Peres, Measures of full dimension on affine-invariant sets, Ergodic Theory and Dynamical Systems, 16 (1996), 307-323.
    • (1996) Ergodic Theory and Dynamical Systems , vol.16 , pp. 307-323
    • Kenyon, R.1    Peres, Y.2
  • 19
    • 0002782396 scopus 로고
    • The singularity spectrum for general sierpinski carpets
    • J. King, The singularity spectrum for general Sierpinski carpets, Advances in Mathematics, 116 (1995), 1-8.
    • (1995) Advances in Mathematics , vol.116 , pp. 1-8
    • King, J.1
  • 21
    • 84972500327 scopus 로고
    • The hausdorff dimension of general sierpinski carpets
    • C. McMullen, The Hausdorff dimension of general Sierpinski carpets, Nagoya Math. J., 96 (1984), 1-9.
    • (1984) Nagoya Math. J. , vol.96 , pp. 1-9
    • McMullen, C.1
  • 22
    • 85027614017 scopus 로고
    • A multifractal formalism
    • L. Olsen, A multifractal formalism, Advances in Mathematics, 116 (1995), 82-196.
    • (1995) Advances in Mathematics , vol.116 , pp. 82-196
    • Olsen, L.1
  • 23
    • 0003344201 scopus 로고
    • Random geometrically graph directed self-similar multifractals
    • Longman Scientific & Technical
    • _, Random geometrically graph directed self-similar multifractals, Pitman Research Notes in Mathematics Series, Vol. 307, Longman Scientific & Technical, 1994.
    • (1994) Pitman Research Notes in Mathematics Series , vol.307
  • 24
    • 84976007415 scopus 로고    scopus 로고
    • The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure
    • to appear
    • Y. Peres, The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure, Math. Proc. Cambridge Phil. Soc., to appear.
    • Math. Proc. Cambridge Phil. Soc.
    • Peres, Y.1
  • 25
    • 84976034033 scopus 로고
    • The packing measure of self-affine carpets
    • _, The packing measure of self-affine carpets, Math. Proc. Cambridge Phil. Soc., 115 (1994), 437-450.
    • (1994) Math. Proc. Cambridge Phil. Soc. , vol.115 , pp. 437-450
  • 26
    • 0039792757 scopus 로고
    • Generalized spectrum for the dimension: The approach based on carathéodory's construction
    • World Sci. Publishing, Teaneck
    • Ya. Pesin, Generalized spectrum for the dimension: The approach based on Carathéodory's construction, in 'Constantin Carathéodory: An international tribute', World Sci. Publishing, Teaneck, (1991), 1108-1119.
    • (1991) Constantin Carathéodory: An International Tribute , pp. 1108-1119
    • Pesin, Ya.1
  • 27
    • 21144463609 scopus 로고
    • On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions
    • _, On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions, Journal of Statistical Physics, 71 (1993), 529-547.
    • (1993) Journal of Statistical Physics , vol.71 , pp. 529-547
  • 33
    • 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 (1992), 367-411.
    • (1992) Indiana Univ. Math. J. , vol.42 , pp. 367-411
    • Strichartz, R.S.1
  • 34
    • 84966224394 scopus 로고
    • Packing measure, and its evaluation for a brownian path
    • S.J. Taylor and C. Tricot, Packing measure, and its evaluation for a Brownian path, Trans. Amer. Math. Soc., 288 (1985), 679-699.
    • (1985) Trans. Amer. Math. Soc. , vol.288 , pp. 679-699
    • Taylor, S.J.1    Tricot, C.2
  • 35
    • 84971877468 scopus 로고
    • Two definitions of fractional dimension
    • C. Tricot, Two definitions of fractional dimension, Math. Proc. Camb. Phil. Soc., 91 (1982), 57-74.
    • (1982) Math. Proc. Camb. Phil. Soc. , vol.91 , pp. 57-74
    • Tricot, C.1
  • 36
    • 84956256298 scopus 로고
    • Dimension, entropy and Lyapunov exponents
    • L.-S. Young, Dimension, entropy and Lyapunov exponents, Ergod. Th. & Dynam. Sys., 2 (1982), 109-124.
    • (1982) Ergod. Th. & Dynam. Sys. , vol.2 , pp. 109-124
    • Young, L.-S.1


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