The Real Fatou Conjecture. (AM-144), Volume 144

A self-contained and complete version of the argument known as the Fatou Conjecture designed for those with no knowledge of complex dynamics and only a basic familiarity with interval maps. The title is number 144 in the ANNALS OF MATHEMATICS series and is suitable for specialists in real dynamics and graduates.

---

In 1920, Pierre Fatou expressed the conjecture that - except for special cases - all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture rematins the main open problem in the dynamics of iterated maps. This volume provides a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis.