Completely invariant Julia sets of polynomial semigroups
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- by Rich Stankewitz PDF
- Proc. Amer. Math. Soc. 127 (1999), 2889-2898 Request permission
Abstract:
Let $G$ be a semigroup of rational functions of degree at least two, under composition of functions. Suppose that $G$ contains two polynomials with non-equal Julia sets. We prove that the smallest closed subset of the Riemann sphere which contains at least three points and is completely invariant under each element of $G$, is the sphere itself.References
- Alan F. Beardon, Iteration of rational functions, Graduate Texts in Mathematics, vol. 132, Springer-Verlag, New York, 1991. Complex analytic dynamical systems. MR 1128089, DOI 10.1007/978-1-4612-4422-6
- A. Hinkkanen and G. J. Martin, The dynamics of semigroups of rational functions. I, Proc. London Math. Soc. (3) 73 (1996), no. 2, 358–384. MR 1397693, DOI 10.1112/plms/s3-73.2.358
Additional Information
- Rich Stankewitz
- Email: rich.stankewitz@math.tamu.edu
- Received by editor(s): March 10, 1997
- Received by editor(s) in revised form: December 8, 1997
- Published electronically: April 23, 1999
- Additional Notes: This research was supported by a Department of Education GAANN fellowship and by the Research Board of the University of Illinois at Urbana-Champaign.
- Communicated by: Albert Baernstein II
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2889-2898
- MSC (1991): Primary 30D05, 58F23
- DOI: https://doi.org/10.1090/S0002-9939-99-04857-1
- MathSciNet review: 1600149