3 papers
math.DS1998
Completely invariant sets of normality for rational semigroups
Rich Stankewitz
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 sp…
math.DS1998
Completely invariant Julia sets of polynomial semigroups
Rich Stankewitz
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…
math.DS1998
Uniformly perfect sets, rational semigroups, Kleinian groups and IFS's
Rich Stankewitz
We show that the Julia set of a non-elementary rational semigroup G is uniformly perfect when there is a uniform bound on the Lipschitz constants of the generators of G. This also…