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Volumn 124, Issue 3, 1998, Pages 531-546

Measure and dimension for some fractal families

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EID: 33746803712     PISSN: 03050041     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0305004198002680     Document Type: Article
Times cited : (180)

References (40)
  • 2
    • 84961493604 scopus 로고
    • A Mandelbrot set for pairs of linear maps
    • M. F. BARNSLEY and A. N. HARRINGTON. A Mandelbrot set for pairs of linear maps. Phisica 15D (1985), 421-432.
    • (1985) Phisica , vol.15 D , pp. 421-432
    • Barnsley, M.F.1    Harrington, A.N.2
  • 4
    • 85034162921 scopus 로고    scopus 로고
    • Power series with restricted coefficients and a root on a given ray
    • F. BEAUCOUP, P. BORWEIN, D. W. BOYD and C. PINNER. Power series with restricted coefficients and a root on a given ray, to appear in Math. Comp.
    • Math. Comp.
    • Beaucoup, F.1    Borwein, P.2    Boyd, D.W.3    Pinner, C.4
  • 5
    • 0000942614 scopus 로고
    • On the fundamental geometrical properties of linearly measurable plane sets of points II
    • A. S. BESICOVITCH. On the fundamental geometrical properties of linearly measurable plane sets of points II. Math. Annalen 115 (1938), 296-329.
    • (1938) Math. Annalen , vol.115 , pp. 296-329
    • Besicovitch, A.S.1
  • 7
    • 21744456350 scopus 로고    scopus 로고
    • Correlation dimension for iterated function systems
    • W. CHIN, B. HUNT and J. A. YORKE. Correlation dimension for iterated function systems. Trans. Amer. Math. Soc. 349 (1997), 1783-1796.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 1783-1796
    • Chin, W.1    Hunt, B.2    Yorke, J.A.3
  • 9
    • 0003292137 scopus 로고
    • The Hausdorff dimension of some fractals and attractors of overlapping construction
    • K. FALCONER. The Hausdorff dimension of some fractals and attractors of overlapping construction. J. Stat. Physics 47, Nos. 1/2, 1987.
    • (1987) J. Stat. Physics , vol.47 , Issue.1-2
    • Falconer, K.1
  • 10
    • 84976003309 scopus 로고
    • The Hausdorff dimension of self-affine fractals
    • K. 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.1
  • 11
    • 84966211167 scopus 로고
    • Dimensions and measures of quasi-self-similar sets
    • K. FALCONER. Dimensions and measures of quasi-self-similar sets. Proc. Amer. Math. Soc. 106 (1989), 543-554.
    • (1989) Proc. Amer. Math. Soc. , vol.106 , pp. 543-554
    • Falconer, K.1
  • 14
    • 21944451974 scopus 로고    scopus 로고
    • The Hausdorff dimension of graphs of Weierstrass functions
    • B. HUNT. The Hausdorff dimension of graphs of Weierstrass functions. Proc. Amer. Math. Soc. 126 (1998), 791-800.
    • (1998) Proc. Amer. Math. Soc. , vol.126 , pp. 791-800
    • Hunt, B.1
  • 15
    • 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
  • 16
  • 17
    • 84974040590 scopus 로고
    • On Hausdorff dimension of projections
    • R. KAUFMAN. On Hausdorff dimension of projections. Mathematika 15 (1968), 153-155.
    • (1968) Mathematika , vol.15 , pp. 153-155
    • Kaufman, R.1
  • 19
    • 0001523338 scopus 로고    scopus 로고
    • Projecting the one-dimensional Sierpinski gasket
    • R. KENYON. Projecting the one-dimensional Sierpinski gasket. Israel J. Math. 97 (1997), 221-238.
    • (1997) Israel J. Math. , vol.97 , pp. 221-238
    • Kenyon, R.1
  • 20
    • 0000416849 scopus 로고
    • On the dimension of some graphs
    • F. LEDRAPPIER. On the dimension of some graphs. Contemporary Math. 135 (1992), 285-293.
    • (1992) Contemporary Math. , vol.135 , pp. 285-293
    • Ledrappier, F.1
  • 21
    • 84963103615 scopus 로고
    • Some fundamental geometrical properties of plane sets of fractional dimensions
    • J. MARSTRAND. Some fundamental geometrical properties of plane sets of fractional dimensions. Proc. London Math. Soc. 4 (1954), 257-302.
    • (1954) Proc. London Math. Soc. , vol.4 , pp. 257-302
    • Marstrand, J.1
  • 22
    • 0000528266 scopus 로고
    • Orthogonal projections, Riesz capacities and Minkowski content
    • P. MATTILA. Orthogonal projections, Riesz capacities and Minkowski content. Indiana University Math. J. 39 (1990), 185-198.
    • (1990) Indiana University Math. J. , vol.39 , pp. 185-198
    • Mattila, P.1
  • 24
    • 0001055201 scopus 로고
    • Zeros of polynomials with 0,1 coefficients
    • A. M. ODLYZKO and B. POONEN. Zeros of polynomials with 0,1 coefficients. L'Enseignement Math. 39 (1993), 317-348.
    • (1993) L'Enseignement Math. , vol.39 , pp. 317-348
    • Odlyzko, A.M.1    Poonen, B.2
  • 25
    • 0010564057 scopus 로고
    • On the β-expansions of real numbers
    • W. PARRY. On the β-expansions of real numbers. Acta Math. Acad. Sci. Hungar. 11 (1960), 401-416.
    • (1960) Acta Math. Acad. Sci. Hungar. , vol.11 , pp. 401-416
    • Parry, W.1
  • 27
    • 0030497277 scopus 로고    scopus 로고
    • Absolute continuity of Bernoulli convolutions, a simple proof
    • Y. PERES and B. SOLOMYAK. Absolute continuity of Bernoulli convolutions, a simple proof. Math. Research Letters 3:2 (1996), 231-239.
    • (1996) Math. Research Letters , vol.3 , Issue.2 , pp. 231-239
    • Peres, Y.1    Solomyak, B.2
  • 28
    • 85013315996 scopus 로고    scopus 로고
    • Self-similar measures and intersections of Cantor sets
    • to appear
    • Y. PERES and B. SOLOMYAK. Self-similar measures and intersections of Cantor sets. Trans. Amer. Math. Soc., to appear.
    • Trans. Amer. Math. Soc.
    • Peres, Y.1    Solomyak, B.2
  • 30
    • 0040341424 scopus 로고
    • Representations for real numbers and their ergodic properties
    • A. RÉNYI. Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957), 477-493.
    • (1957) Acta Math. Acad. Sci. Hungar. , vol.8 , pp. 477-493
    • Rényi, A.1
  • 31
    • 0000922897 scopus 로고
    • The Hausdorff dimension of λ-expansions with deleted digits
    • M. POLLICOTT and K. SIMON. The Hausdorff dimension of λ-expansions with deleted digits. Trans. Amer. Math. Soc. 347 (1995), 967-983.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 967-983
    • Pollicott, M.1    Simon, K.2
  • 32
    • 0000690674 scopus 로고
    • On Hausdorff dimension of some fractal sets
    • F. PRZYTYCKI and M. URBAŃSKI. On Hausdorff dimension of some fractal sets. Studia Mathematica 93 (1989), 155-186.
    • (1989) Studia Mathematica , vol.93 , pp. 155-186
    • Przytycki, F.1    Urbański, M.2
  • 33
    • 84966239752 scopus 로고
    • Separation properties for self-similar sets
    • A. SCHIEF. Separation properties for self-similar sets. Proc. Amer. Math. Soc. 122 (1994), 111-115.
    • (1994) Proc. Amer. Math. Soc. , vol.122 , pp. 111-115
    • Schief, A.1
  • 34
    • 0000561288 scopus 로고    scopus 로고
    • Most β shifts have bad ergodic properties
    • J. SCHMELING. Most β shifts have bad ergodic properties. Ergodic Th. Dynam. Sys. 17 (1997), 675-694.
    • (1997) Ergodic Th. Dynam. Sys. , vol.17 , pp. 675-694
    • Schmeling, J.1
  • 35
    • 0000351341 scopus 로고
    • Algebraic integers whose conjugates lie in the unit circle
    • C. L. SIEGEL. Algebraic integers whose conjugates lie in the unit circle. Duke Math. J. 11 (1944), 597-602.
    • (1944) Duke Math. J. , vol.11 , pp. 597-602
    • Siegel, C.L.1
  • 36
    • 0003310263 scopus 로고
    • Hausdorff dimension for non-invertible maps
    • K. SIMON. Hausdorff dimension for non-invertible maps. Ergodic Th. Dynam. Sys. 13 (1993), 199-212.
    • (1993) Ergodic Th. Dynam. Sys. , vol.13 , pp. 199-212
    • Simon, K.1
  • 37
    • 0000155997 scopus 로고    scopus 로고
    • Overlapping cylinders: The size of a dynamically defined Cantor-set
    • d-Actions
    • d-Actions, LMS Lecture Notes Series 228 (1996), 259-272.
    • (1996) LMS Lecture Notes Series , vol.228 , pp. 259-272
    • Simon, K.1
  • 38
    • 84963057031 scopus 로고
    • Conjugates of beta-numbers and the zero-free domain for a class of analytic functions
    • B. SOLOMYAK. Conjugates of beta-numbers and the zero-free domain for a class of analytic functions. Proc. London Math. Soc. 68 (1994), 477-498.
    • (1994) Proc. London Math. Soc. , vol.68 , pp. 477-498
    • Solomyak, B.1
  • 39
    • 0000660967 scopus 로고
    • 1 (an Erdös problem)
    • 1 (an Erdös problem). Annals of Math. 142 (1995), 611-625.
    • (1995) Annals of Math. , vol.142 , pp. 611-625
    • Solomyak, B.1
  • 40
    • 0000826876 scopus 로고
    • A simple example of a continuous function without derivative
    • T. TAKAGI. A simple example of a continuous function without derivative. Proc. Phys. Math. Soc. Japan 1 (1903), 176-177.
    • (1903) Proc. Phys. Math. Soc. Japan , vol.1 , pp. 176-177
    • Takagi, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.