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1997 | 154 | 3 | 207-260
Tytuł artykułu

Branched coverings and cubic Newton maps

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We construct branched coverings such as matings and captures to describe the dynamics of every critically finite cubic Newton map. This gives a combinatorial model of the set of cubic Newton maps as the gluing of a subset of cubic polynomials with a part of the filled Julia set of a specific polynomial (Figure 1).
Słowa kluczowe
Rocznik
Tom
154
Numer
3
Strony
207-260
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-12-05
poprawiono
1996-09-09
poprawiono
1997-04-01
poprawiono
1997-05-22
Twórcy
autor
Bibliografia
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  • [D3] A. Douady, Chirurgie sur les applications holomorphes, in: Proc. Internat. Congress Math., Berkeley, Calif., 1986, 724-738 (English version: preprint MSRI, 1986).
  • [DH1] A. Douady et J. H. Hubbard, Étude dynamique des polynômes complexes, I et II, avec la collaboration de P. Lavaurs, Tan Lei et P. Sentenac, Publication d'Orsay 84-02, 85-04, 1984/1985.
  • [DH2] A. Douady et J. H. Hubbard, A proof of Thurston's topological characterization of rational functions, Acta Math. 171 (1993), 263-297.
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  • [F] D. Faught, Local connectivity in a family of cubic polynomials, Ph.D. thesis, Cornell Univ., Ithaca, N.Y., 1992.
  • [Ha] F. von Haeseler, Über Attraktionsgebiete superattraktiver Zykle, Ph.D. thesis, Bremen Univ., Bremen, 1985.
  • [HP] F. von Haeseler and H.-O. Peitgen, Newton's method and complex dynamical systems, Acta Appl. Math. 13 (1988), 3-58.
  • [He] J. Head, The combinatorics of Newton's method for cubic polynomials, Ph.D. thesis, Cornell Univ., Ithaca, N.Y., 1987.
  • [Le] S. Levy, Critically finite rational maps, Ph.D. Thesis, Princeton Univ., Princeton, N.J., 1985.
  • [Me] H.-G. Meier, On the connectedness of the Julia-set for rational functions, preprint, Aachen Univ., 1989.
  • [M1] J. Milnor, On cubic polynomials with periodic critical point (very rough draft), 5-28-91.
  • [M2] J. Milnor, Dynamics in one complex variable: Introductory lectures, preprint Stony Brook 1990-5.
  • [Prz] F. Przytycki, Remarks on the simple connectedness of basins of sinks for iterations of rational maps, in: Dynamical Systems and Ergodic Theory, K. Krzyżewski (ed.), PWN-Polish Sci. Publ., 1989, 229-235.
  • [R1] M. Rees, A partial description of parameter space of rational maps of degree two: Part I, Acta Math. 168 (1992), 11-87.
  • [R2] M. Rees, A partial description of parameter space of rational maps of degree two: Part II, Proc. London Math. Soc. (3) 70 (1995), 644-690.
  • [R3] M. Rees, Realization of matings of polynomials as rational maps of degree two, manuscript, 1986.
  • [Sa] D. Saupe, Discrete versus continuous Newton's method: A case study, Acta Appl. Math. 13 (1988), 59-80.
  • [Sh1] M. Shishikura, The connectivity of the Julia set of rational maps and Fixed points, preprint, I.H.E.S., Bures-sur-Yvette, 1990.
  • [Sh2] M. Shishikura, On a theorem of M. Rees for matings of polynomials, preprint, I.H.E.S., Bures-sur-Yvette, 1990.
  • [ST] M. Shishikura and L. Tan, A family of cubic rational maps and matings of cubic polynomials, preprint 88-50, Max-Planck-Institut für Mathematik, Bonn.
  • [Ta] L. Tan, Matings of quadratic polynomials, Ergodic Theory Dynam. Systems 12 (1992), 589-620.
  • [TY] L. Tan and Y. C. Yin, Local connectivity of the Julia set for geometrically finite rational maps, Sci. in China (Ser. A) 39 (1) (1996), 39-47.
  • [Th] W. Thurston, The combinatorics of iterated rational maps, preprint, Princeton Univ., Princeton, N.J., 1983.
  • [W] B. Wittner, On the bifurcation loci of rational maps of degree two, Ph.D. thesis, Cornell Univ., Ithaca, N.Y., 1986.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv154i3p207bwm
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