English

Completely invariant Julia sets of polynomial semigroups

Dynamical Systems 2007-05-23 v1 Complex Variables

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.

Keywords

Cite

@article{arxiv.math/9810090,
  title  = {Completely invariant Julia sets of polynomial semigroups},
  author = {Rich Stankewitz},
  journal= {arXiv preprint arXiv:math/9810090},
  year   = {2007}
}

Comments

10 pages