No-wandering-domain theorem

The No wandering domain theorem by D Sullivan proves that a rational map has no wandering domain, e.g. there is no set $U$ 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, Springer 1993, ISBN 0-387-97942-5

External links

• http://www.math.qc.edu/~zakeri/notes/wander.pdf