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Volumn 36, Issue 2, 1999, Pages 417-435

Generalized computation of Schröder iteration functions to motivate families of Julia and Mandelbrot-like sets

Author keywords

Critical point; Fatou set; Iteration; Julia set; Schr der's method

Indexed keywords


EID: 0004309972     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997317365     Document Type: Article
Times cited : (17)

References (14)
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    • N. ARGYROPOULOS, A. BÖHM, AND V. DRAKOPOULOS, Julia and Mandelbrot-like sets for higher order König rational iteration functions, in Fractal Frontiers, M. M. Novak and T. G. Dewey, eds., World Scientific, Singapore, 1997, pp. 169-178.
    • (1997) Fractal Frontiers , pp. 169-178
    • Argyropoulos, N.1    Böhm, A.2    Drakopoulos, V.3
  • 2
    • 0000519586 scopus 로고
    • On the iteration of a rational function: Computer experiments with Newton's method
    • J. H. CURRY, L. GARNETT, AND D. R. SULLIVAN, On the iteration of a rational function: Computer experiments with Newton's method, Comm. Math. Phys., 91 (1983), pp. 267-277.
    • (1983) Comm. Math. Phys. , vol.91 , pp. 267-277
    • Curry, J.H.1    Garnett, L.2    Sullivan, D.R.3
  • 3
    • 0001539882 scopus 로고
    • On the dynamics of polynomial-like mappings
    • A. DOUADY AND J. H. HUBBARD, On the dynamics of polynomial-like mappings, Ann. Sci. École Norm. Sup., 18 (1985), pp. 287-343.
    • (1985) Ann. Sci. École Norm. Sup. , vol.18 , pp. 287-343
    • Douady, A.1    Hubbard, J.H.2
  • 4
    • 0032180592 scopus 로고    scopus 로고
    • On the additional fixed points of Schröder iteration functions associated with a one-parameter family of cubic polynomials
    • V. DRAKOPOULOS, On the additional fixed points of Schröder iteration functions associated with a one-parameter family of cubic polynomials, Comput. & Graphics, 22 (1998), pp. 629-634.
    • (1998) Comput. & Graphics , vol.22 , pp. 629-634
    • Drakopoulos, V.1
  • 6
    • 0000888015 scopus 로고
    • Sur les équations fonctionelles
    • M. P. FATOU, Sur les équations fonctionelles, Bull. Soc. Math. France, 47 (1919), pp. 161-271; 48 (1920), pp. 33-94, 208-314.
    • (1919) Bull. Soc. Math. France , vol.47 , pp. 161-271
    • Fatou, M.P.1
  • 7
    • 0001661194 scopus 로고
    • M. P. FATOU, Sur les équations fonctionelles, Bull. Soc. Math. France, 47 (1919), pp. 161-271; 48 (1920), pp. 33-94, 208-314.
    • (1920) Bull. Soc. Math. France , vol.48 , pp. 33-94
  • 8
    • 84966204219 scopus 로고
    • Schröder and Trudi: A historical excursion
    • A. S. HOUSEHOLDER, Schröder and Trudi: A historical excursion, SIAM Rev., 16 (1974), pp. 344-348.
    • (1974) SIAM Rev. , vol.16 , pp. 344-348
    • Householder, A.S.1
  • 10
    • 0002413379 scopus 로고
    • Mémoire sur l'itération des fonctions rationelles
    • G. JULIA, Mémoire sur l'itération des fonctions rationelles, J. Math. Pures Appl., 8 (1918), pp. 47-245.
    • (1918) J. Math. Pures Appl. , vol.8 , pp. 47-245
    • Julia, G.1
  • 13
    • 34447609127 scopus 로고
    • Über unendlich viele Algorithmen zur Auflösung der Gleichungen
    • E. SCHRÖDER, Über unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Ann., 2 (1870), pp. 317-365.
    • (1870) Math. Ann. , vol.2 , pp. 317-365
    • Schröder, E.1
  • 14
    • 84966240099 scopus 로고
    • Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: A computer assisted study
    • E. R. VRSCAY, Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: A computer assisted study, Math. Comp., 46 (1986), pp. 151-169.
    • (1986) Math. Comp. , vol.46 , pp. 151-169
    • Vrscay, E.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.