No-wandering-domain theorem

The no wandering domain theorem by Dennis Sullivan states that a rational map has no wandering domain, i.e., there is no domain $U$ in the Fatou set of $f$ such that $U,f(U),f(f(U)),\dots ,f^{k}(U)$ are all disjoint.

References

• Lennart Carleson and Theodore W. Gamelin, Complex Dynamics, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993, ISBN 0-387-97942-5 MR1230383
• Dennis Sullivan, Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains, Annals of Mathematics 122 (1985), no. 3, 401--418. MR0819553

External links

• Sullivan's proof of Fatou's no wandering domain conjecture by S. Zakeri