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Cayley’s problem and Julia sets

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References

  1. Ahlfors, L. V.Complex analysis, New York: McGraw-Hill 1966

    MATH  Google Scholar 

  2. Brolin, H., (1967) “Invariant sets under iteration of rational functions”,Arkiv für Matematik 6, 103–144

    Article  MathSciNet  Google Scholar 

  3. Cayley, A., (1879) “The Newton-Fourier imaginary problem”,Am. J. Math. II, 97

    MathSciNet  Google Scholar 

  4. Cayley, A., (1879) “Application of the Newton-Fourier Method to an imaginary root of an equation”,Quaterly Journal of Pure and Applied Mathematics XVI, 179–185

    MATH  Google Scholar 

  5. Cayley, A., (1890) “Sur les racines d’une équation algébrique”,CRAS 110, 215–218

    MATH  Google Scholar 

  6. Cremer, H., (1925) “Über die Iteration rationaler Funktionen”,Jber. d. Dt. Math.-Verein. 33, 185–210

    MATH  Google Scholar 

  7. Douady, A., (1982/83) “Systèmes dynamiques holomorphes”,Séminaire Bourbaki, Nr. 599

  8. Fatou, P.(1919, 1920) “Sur les équations fonctionelles”,Bull. Soc. Math. France 47, 161–271,48, 33–94, 208–314

    MathSciNet  Google Scholar 

  9. Guckenheimer, J., (1968) “Endomorphisms of the Riemann sphere”, in:Global Analysis (S.-S. Chern, S. Smale, eds.), 95-123.

  10. Julia, G., (1918) “Mémoire sur l’itération des fonctions rationnelles”,J. de Math. pures et appliquées, sér. 8.1, 47- 245.

    Google Scholar 

  11. Lattès, M. S., (1918) “Sur l’itération des substitutions rationnelles et les fonctions de Poincaré“,C.R.A.S. 166, 26–28

    MATH  Google Scholar 

  12. Mandelbrot, B., (1982)The fractal geometry of nature, San Francisco: Freeman

    MATH  Google Scholar 

  13. Moser, J. K., (1962) “On invariant curves of area-preserving mappings of an annulus”,Nach. Akad. Wiss. Gött. Math. Klass., 1-20

  14. Peitgen, H.-O., Saupe, D., v. Haeseler, F., (1983) “Newton’s Method and Julia sets”, Universität Bremen, Forschungsschwerpunkt ‘Dynamische Systeme’, Report Nr. 104

  15. Ruelle, D., (1981) “Repellers for real analytic maps”, preprint, IHES

  16. Rüssmann, H., (1970) “Kleine Nenner I. Über invariante Kurven differenzierbarer Abbildungen eines Kreisringes”,Nach. Akad. Wiss. Gött. Math. Klass. 68–105

  17. Rüssmann, H., (1972) “Kleine Nenner II. Bemerkungen zur Newton’schen Methode”,Nachr. Akad. Wiss. Göttingen,Math. Phys. Kl, 1–20

  18. Smale, S., (1981) “The fundamental theorem of algebra and complexity theory”,Bull. AMS 4, 1–36

    Article  MATH  MathSciNet  Google Scholar 

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Peitgen, H.O., Saupe, D. & Haeseler, F.v. Cayley’s problem and Julia sets. The Mathematical Intelligencer 6, 11–20 (1984). https://doi.org/10.1007/BF03024150

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