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Volumn 37, Issue 1-3, 1998, Pages 81-99

Geometric constructions in multifractal geometry

Author keywords

Fractals; Intersections of measures Hausdorff dimension; Multifractals; Packing dimension; Slices of measures

Indexed keywords


EID: 54649083462     PISSN: 00315303     EISSN: 15882829     Source Type: Journal    
DOI: 10.1023/a:1004730520036     Document Type: Review
Times cited : (7)

References (46)
  • 1
    • 0002387490 scopus 로고    scopus 로고
    • Random self-similar multifractals
    • [AP] M. ARBEITER and N. PATZSCHKE, Random self-similar multifractals Math. Nachr. 181 (1996), 5-42.
    • (1996) Math. Nachr. , vol.181 , pp. 5-42
    • Arbeiter, M.1    Patzschke, N.2
  • 2
  • 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
  • 6
    • 0003211662 scopus 로고
    • Analysis of and on uniformly rectifiable sets
    • American Mathematical Society, Providence, RI
    • [DS] G. DAVID and S. SEMMES, Analysis Of and On Uniformly Rectifiable Sets, Mathematical Surveys and Monographs, 38. American Mathematical Society, Providence, RI, 1993.
    • (1993) Mathematical Surveys and Monographs , vol.38
    • David, G.1    Semmes, S.2
  • 7
    • 84962991716 scopus 로고
    • Multifractal decompositions of digraph recursive fractals
    • [EM] 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
  • 11
    • 84975964787 scopus 로고
    • On the dimension of product measures
    • [Ha2] H. HAASE, On the dimension of product measures, Mathematika 37 (1990), 316-323.
    • (1990) Mathematika , vol.37 , pp. 316-323
    • Haase, H.1
  • 12
    • 3342916075 scopus 로고
    • Fractal measures and their singularities: The characterization of strange sets
    • [HJKPS] T. C. HALSEY, M. H. JENSEN, L. P. KADANOEF, 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    Kadanoef, L.P.3    Procaccia, I.4    Shraiman, B.J.5
  • 13
    • 54749109648 scopus 로고    scopus 로고
    • On Hausdorff and packing dimension of product spaces
    • to appear
    • [Ho] J. HOWROYD, On Hausdorff and packing dimension of product spaces, Math. Proc. Camb. Phil. Soc. (to appear).
    • Math. Proc. Camb. Phil. Soc.
    • Howroyd, J.1
  • 15
    • 77956809951 scopus 로고
    • Sur la dimension des intersections
    • ed. J. A. Barroso, Elsevier Science Publishers B. V.
    • [Ka] J.-P. KAHANE, Sur la dimension des intersections, in Aspects of Mathematics and its Applications, ed. J. A. Barroso, Elsevier Science Publishers B. V. 1986, pp. 419-430.
    • (1986) Aspects of Mathematics and Its Applications , pp. 419-430
    • Kahane, J.-P.1
  • 17
    • 0000921510 scopus 로고
    • Singularity spectrum for recurrent IFS attractors
    • [KG] J. KING and J. S. GERONIMO, Singularity spectrum for recurrent IFS attractors, Nonlinearity 6 (1992), 337-348.
    • (1992) Nonlinearity , vol.6 , pp. 337-348
    • King, J.1    Geronimo, J.S.2
  • 18
    • 0009126883 scopus 로고
    • p-spectrum and multifractal formalism
    • Proceedings, Fractal Geometry and Stochastics, Finsterbergen, Germany, June. (Editors C. Bandt, S. Graf and M. Zähle). Birkhäuser Verlag
    • p-spectrum and multifractal formalism, Proceedings, Fractal Geometry and Stochastics, Finsterbergen, Germany, June, 1994. Progess in Probability 37 (Editors C. Bandt, S. Graf and M. Zähle), pp. 55-90. Birkhäuser Verlag, 1995.
    • (1994) Progess in Probability , vol.37 , pp. 55-90
    • Lau, K.S.1
  • 19
    • 0008998845 scopus 로고
    • The dimension spectrum of the maximal measure
    • [Lo1] A. O. LOPES, The dimension spectrum of the maximal measure SIAM jour. Math. Anat. 20 (1989), 1243-1254.
    • (1989) SIAM Jour. Math. Anat. , vol.20 , pp. 1243-1254
    • Lopes, A.O.1
  • 20
    • 38249016198 scopus 로고
    • Dimension spectra and a mathematical model for phase transition
    • [Lo2] A. O. LOPES, Dimension spectra and a mathematical model for phase transition Advances in Applied Mathematics 1 (1990), 475-502.
    • (1990) Advances in Applied Mathematics , vol.1 , pp. 475-502
    • Lopes, A.O.1
  • 22
    • 0013167960 scopus 로고
    • The dimension of Cartesian product sets
    • [Mar1] J. M. MARSTRAND, The dimension of Cartesian product sets, Proc. Lond. Math. Soc. 50 (1954), 198-206.
    • (1954) Proc. Lond. Math. Soc. , vol.50 , pp. 198-206
    • Marstrand, J.M.1
  • 23
    • 84963103615 scopus 로고
    • Some fundamental geometrical properties of plane sets of fractional dimensions
    • [Mar2] J. M. MARSTRAND, Some fundamental geometrical properties of plane sets of fractional dimensions, Proc. Lond. Math. Soc. 4 (1954), 257-302.
    • (1954) Proc. Lond. Math. Soc. , vol.4 , pp. 257-302
    • Marstrand, J.M.1
  • 24
    • 0000367680 scopus 로고
    • Hausdorff dimension, othogonal projections and intersections with planes
    • [Mat1] P. MATTILA, Hausdorff dimension, othogonal projections and intersections with planes, Ann. Acad. Sci. Fenn. Series A. I. Mathematica 1 (1975), 227-244.
    • (1975) Ann. Acad. Sci. Fenn. Series A. I. Mathematica , vol.1 , pp. 227-244
    • Mattila, P.1
  • 25
    • 0003023698 scopus 로고
    • Hausdorff dimension and capacities of intersections of sets in n-space
    • [Mat2] P. MATTILA, Hausdorff dimension and capacities of intersections of sets in n-space, Acta Math. 152 (1984), 77-105.
    • (1984) Acta Math. , vol.152 , pp. 77-105
    • Mattila, P.1
  • 28
    • 85027614017 scopus 로고
    • A multifractal formalism
    • [OI1] L. OLSEN, A multifractal formalism, Advances in Mathematics 116 (1995), 82-196.
    • (1995) Advances in Mathematics , vol.116 , pp. 82-196
    • Olsen, L.1
  • 31
    • 21444435010 scopus 로고    scopus 로고
    • Multifractal dimensions of product measures
    • [OI4] L. OLSEN, Multifractal dimensions of product measures, Math. Proc. Camb. Phil. Soc. 120 (1996), 709-734.
    • (1996) Math. Proc. Camb. Phil. Soc. , vol.120 , pp. 709-734
    • Olsen, L.1
  • 37
    • 0001334913 scopus 로고
    • Dimension type characteristics for invariant sets of dynamical systems
    • [Pes1] Y. PESIN, Dimension type characteristics for invariant sets of dynamical systems, Russian Math. Surveys 43 (1988), 111-151.
    • (1988) Russian Math. Surveys , vol.43 , pp. 111-151
    • Pesin, Y.1
  • 38
    • 0039792757 scopus 로고
    • Generalized spectrum for the dimension: The approach based on Carathéodory's construction
    • World Sci. Publishing, Teaneck
    • [Pes2] Y. PESIN, Generalized spectrum for the dimension: the approach based on Carathéodory's construction, in: Constantin Carathéodory: an international tribute, pp. 1108-1119, World Sci. Publishing, Teaneck, 1991.
    • (1991) Constantin Carathéodory: An International Tribute , pp. 1108-1119
    • Pesin, Y.1
  • 40
    • 21444441654 scopus 로고    scopus 로고
    • A multifractal analysis of equilibrium measures for conformal expanding maps and Markov Moran geometric constructions
    • [PW] Y. PESIN and H. WEISS, A multifractal analysis of equilibrium measures for conformal expanding maps and Markov Moran geometric constructions, J. Statist. Phys. 86 (1997), 233-275.
    • (1997) J. Statist. Phys. , vol.86 , pp. 233-275
    • Pesin, Y.1    Weiss, H.2
  • 41
    • 84974252535 scopus 로고
    • The singularity spectrum f(α) for cookie-cutters
    • [Ra] D. RAND, The singularity spectrum f(α) for cookie-cutters, Ergodic Theory and Dynamical Systems 9 (1989), 527-541.
    • (1989) Ergodic Theory and Dynamical Systems , vol.9 , pp. 527-541
    • Rand, D.1
  • 44
    • 0004136765 scopus 로고
    • Princeton University Press
    • [St] E. STEIN, Harmonic Analysis, Princeton University Press, 1993.
    • (1993) Harmonic Analysis
    • Stein, E.1
  • 45
    • 84966224394 scopus 로고
    • Packing measure, and its evaluation for a Brownian path
    • [TT] 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
  • 46
    • 84971877468 scopus 로고
    • Two definitions of fractional dimension
    • [Tr] 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


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