Completely invariant sets of normality for rational semigroups

Details Completely invariant sets of normality for rational semigroups Completely invariant sets of normality for rational semigroups

1998-10-15

arxiv.org/abs/math/9810099v1

Mathematics

Dynamical Systems

8 pages

Scientific paper

Let G be a semigroup of rational functions of degree at least two where the
semigroup operation is composition of functions. We prove that the largest open
subset of the Riemann sphere on which the semigroup G is normal and is
completely invariant under each element of G, can have only 0, 1, 2, or
infinitely many components.

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