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Volumn 147, Issue 2, 1998, Pages 225-267

The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets

(1)  Shishikura, Mitsuhiro a  

a NONE

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EID: 0032392257     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121009     Document Type: Article
Times cited : (207)

References (27)
  • 2
    • 0001870459 scopus 로고
    • The dynamics of the Hénon map
    • M. BENEDICKS and L. CARLESON, The dynamics of the Hénon map, Ann. of Math. 133 (1991), 73-169.
    • (1991) Ann. of Math. , vol.133 , pp. 73-169
    • Benedicks, M.1    Carleson, L.2
  • 3
    • 84968494997 scopus 로고
    • Complex analytic dynamics on the Riemann sphere
    • P. BLANCHARD, Complex analytic dynamics on the Riemann sphere, Bull. A. M. S. 11 (1984), 85-141.
    • (1984) Bull. A. M. S. , vol.11 , pp. 85-141
    • Blanchard, P.1
  • 4
    • 27544514665 scopus 로고
    • Holomorphic families of injections
    • L. BERS and H. L. ROYDEN, Holomorphic families of injections, Acta Math. 157 (1986), 259-286.
    • (1986) Acta Math. , vol.157 , pp. 259-286
    • Bers, L.1    Royden, H.L.2
  • 5
    • 85009367586 scopus 로고
    • Equilibrium states and the ergodic theory of Anosov diffeomorphisms
    • Springer, Berlin
    • R. BOWEN, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math. 470, Springer, Berlin, 1975.
    • (1975) Lecture Notes in Math. , vol.470
    • Bowen, R.1
  • 6
    • 51249186941 scopus 로고
    • Hausdorff dimension of quasi-circles
    • _, Hausdorff dimension of quasi-circles, Publ. Math. I.H.E.S. 50 (1979), 11-26.
    • (1979) Publ. Math. I.H.E.S. , vol.50 , pp. 11-26
  • 7
    • 0003206472 scopus 로고
    • Étude dynamique des polynômes complexes
    • 1er partie
    • A. DOUADY and J. H. HUBBARD, Étude dynamique des polynômes complexes, Publ. Math. d'Orsay, 1er partie, 84-02 (1984); 2me partie, 85-04 (1985).
    • (1984) Publ. Math. d'Orsay , pp. 84-102
    • Douady, A.1    Hubbard, J.H.2
  • 8
    • 0039439325 scopus 로고
    • 2me partie
    • A. DOUADY and J. H. HUBBARD, Étude dynamique des polynômes complexes, Publ. Math. d'Orsay, 1er partie, 84-02 (1984); 2me partie, 85-04 (1985).
    • (1985) Publ. Math. d'Orsay , pp. 85-104
  • 9
    • 0002053804 scopus 로고
    • Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
    • M. JAKOBSON, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88.
    • (1981) Comm. Math. Phys. , vol.81 , pp. 39-88
    • Jakobson, M.1
  • 11
    • 0010037084 scopus 로고
    • An analysis of stability of the dynamics of rational functions
    • M. YU. LYUBICH, An analysis of stability of the dynamics of rational functions, Selecta Mathematica Sovietica 9 (1990), 69-90.
    • (1990) Selecta Mathematica Sovietica , vol.9 , pp. 69-90
    • Lyubich, M.Yu.1
  • 13
    • 0040624660 scopus 로고
    • On the dynamics of iterated maps V: Conjecture that the boundary of the M-set has a fractal dimension equal to 2
    • Eds. Fischer and Smith, Marcel Dekker
    • B. MANDELBROT, On the dynamics of iterated maps V: Conjecture that the boundary of the M-set has a fractal dimension equal to 2, in Chaos, Fractals and Dynamics, Eds. Fischer and Smith, Marcel Dekker, 1985, 235-238.
    • (1985) Chaos, Fractals and Dynamics , pp. 235-238
    • Mandelbrot, B.1
  • 14
    • 84967773772 scopus 로고
    • Area and Hausdorff dimension of Julia sets of entire functions
    • C. MCMULLEN, Area and Hausdorff dimension of Julia sets of entire functions, Trans. A. M. S. 300 (1987), 329-342.
    • (1987) Trans. A. M. S. , vol.300 , pp. 329-342
    • McMullen, C.1
  • 16
    • 0011549927 scopus 로고
    • Self-similarity and hairiness in the mandelbrot set
    • Computers in Geometry and Topology, ed. M. C. Tangora, Marcel Dekker
    • _, Self-similarity and hairiness in the Mandelbrot set, in Computers in Geometry and Topology, ed. M. C. Tangora, Lect. Notes in Pure and Appl. Math., Marcel Dekker, Vol. 114 (1989), 211-257.
    • (1989) Lect. Notes in Pure and Appl. Math. , vol.114 , pp. 211-257
  • 18
    • 0003880196 scopus 로고
    • Vandenhoeck & Ruprecht, Göttingen, Germany
    • CH. POMMERENKE, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, Germany, 1975.
    • (1975) Univalent Functions
    • Pommerenke, Ch.1
  • 19
    • 0001243305 scopus 로고
    • Positive measure sets of ergodic rational maps
    • M. REES, Positive measure sets of ergodic rational maps, Ann. Scient. Ec. Norm. Sup., (4) 19 (1986), 383-407.
    • (1986) Ann. Scient. Ec. Norm. Sup., (4) , vol.19 , pp. 383-407
    • Rees, M.1
  • 20
    • 84926802106 scopus 로고
    • Repellers for real analytic maps
    • D. RUELLE, Repellers for real analytic maps, Erg. Th. & Dynam. Sys. 2 (1982), 99-107.
    • (1982) Erg. Th. & Dynam. Sys. , vol.2 , pp. 99-107
    • Ruelle, D.1
  • 22
    • 0040657965 scopus 로고
    • The boundary of the Mandelbrot set has Hausdorff dimension two
    • eds. C. Camacho et al., Astérisque
    • _, The boundary of the Mandelbrot set has Hausdorff dimension two, in Complex Analytic Methods in Dynamical Systems, eds. C. Camacho et al., Astérisque, 222 (1994), 389-405.
    • (1994) Complex Analytic Methods in Dynamical Systems , vol.222 , pp. 389-405
  • 24
    • 27544481771 scopus 로고
    • Extending holomorphic motions
    • D. SULLIVAN and W.P. THURSTON, Extending holomorphic motions, Acta Math. 157 (1986), 243-257.
    • (1986) Acta Math. , vol.157 , pp. 243-257
    • Sullivan, D.1    Thurston, W.P.2
  • 25
    • 0000624194 scopus 로고
    • Conformal dynamical systems
    • Geometric Dynamics, Springer, Berlin
    • D. SULLIVAN, Conformal dynamical systems, in Geometric Dynamics, Lecture note in Math. 1007 (1983), 725-752, Springer, Berlin.
    • (1983) Lecture Note in Math. , vol.1007 , pp. 725-752
    • Sullivan, D.1
  • 26
    • 34249963080 scopus 로고
    • Similarity between the Mandelbrot set and Julia sets
    • TAN LEI, Similarity between the Mandelbrot set and Julia sets, Commun. Math. Phys. 134 (1990), 587-617.
    • (1990) Commun. Math. Phys. , vol.134 , pp. 587-617
    • Tan, L.E.I.1
  • 27
    • 0002867478 scopus 로고
    • Linéarisation des germes de difféomorphismes holomorphes de (ℂ, 0)
    • Sér. I
    • J.-C. YOCCOZ, Linéarisation des germes de difféomorphismes holomorphes de (ℂ, 0), C. R. Acad. Sci. Paris, t.306 (1988), Sér. I, 55-58.
    • (1988) C. R. Acad. Sci. Paris , vol.T.306 , pp. 55-58
    • Yoccoz, J.-C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.