Completely invariant Julia sets of polynomial semigroups

Details Completely invariant Julia sets of polynomial semigroups Completely invariant Julia sets of polynomial semigroups

1998-10-14

arxiv.org/abs/math/9810090v1

Mathematics

Dynamical Systems

10 pages

Scientific paper

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.

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