Dynamic classification of escape time Sierpiński curve Julia sets

Volume 202 / 2009

Robert L. Devaney, Kevin M. Pilgrim Fundamenta Mathematicae 202 (2009), 181-198 MSC: Primary 37F10; Secondary 37F45. DOI: 10.4064/fm202-2-5


For $n \geq 2$, the family of rational maps $F_\lambda(z) = z^n + \lambda/z^n$ contains a countably infinite set of parameter values for which all critical orbits eventually land after some number $\kappa$ of iterations on the point at infinity. The Julia sets of such maps are Sierpiński curves if $\kappa \geq 3$. We show that two such maps are topologically conjugate on their Julia sets if and only if they are Möbius or anti-Möbius conjugate, and we give a precise count of the number of topological conjugacy classes as a function of $n$ and $\kappa$.


  • Robert L. DevaneyDepartment of Mathematics
    Boston University
    Boston, MA 02215, U.S.A.
  • Kevin M. PilgrimDepartment of Mathematics
    Indiana University
    Bloomington, IN 47405, U.S.A.

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