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Cubic Rational Maps with Escaping Critical Points, Part I: Julia Set Dichotomy in the Case of an Attracting Fixed Point

  • Jun Hu [1] ; Arkady Etkin [2]
    1. [1] Brooklyn College of CUNY & Graduate Center of CUNY
    2. [2] Graduate Center of CUNY
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
  • Idioma: inglés
  • Enlaces
  • Resumen
    • The Julia set of any quadratic rational map is either connected or a Cantor set. In this paper, we extend this dichotomy to any cubic rational map with all critical points escaping to an attracting fixed point.

  • Referencias bibliográficas
    • 1. Ahlfors, L.V.: Lectures on quasiconformal mappings. Jr. Van Nostrand Mathematical Studies, 10, D. Van Nostrand co., Inc., Toronto, Ont.-New...
    • 2. Beardon, A.: Iteration of Rational Functions. Springer, New York (1991)
    • 3. Devaney, R.L., Look, D.M., Uminsky, D.: The escape trichotomy for singularly perturbed rational maps. Indiana Univ. Math. Jour. 54, 1621–1634...
    • 4. Hu, J., Etkin, A.: Julia sets of cubic rational maps with escaping critical points. Arnold Math. J. 6, 431–457 (2020)
    • 5. Hu, J., Jimenez, F.G., Muzician, O.: Rational maps with half symmetries, Julia sets, and Multibrot sets in parameter planes. Contemp. Math....
    • 6. Hu, J., Muzician O., Xiao, Y.: Dynamics of regularly ramified rational maps: I. Julia sets of maps in one-parameter families. Discret....
    • 7. McMullen, C.: Automorphisms of rational maps. Holomorphic Functions and Moduli - Vol. I. (Math. Sci. Res. Inst. Publ. 10), 31-60, Springer,...
    • 8. Milnor, J.: On rational maps with two critical points. Exp. Math. 9, 481–522 (2000)
    • 9. Shishikura, M.: On the quasiconformal surgery of rational functions. Ann. Sci. Ec. Norm. Sup. 20, 1–29 (1987)
    • 10. Sullivan, D.: Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains. Ann. Math. 122(3),...
    • 11. Xiao, Y., Qiu, W., Yin, Y.: On the dynamics of generalized McMullen maps. Ergod. Th. Dyn. Sys. 34, 2093–2112 (2014)

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