The main objective of this section is to present a proof of Theorem 1.3. So we assume that unimodal polynomials*f*and*odd*periodic orbits on the real line. These are topological assumptions and if*f*satisfies them than its both fixed points are repelling,*f*has orbits with infinitely many different periods (Sharkovski’s theorem) and the first return time to the restrictive interval is greater than 2.

In the proof Theorem 1.3 a major issue is the choice of domains of analytic continuations of branches

EP - 142 PB - Princeton University Press PY - 1998 SN - 9780691002583 SP - 109 T2 - The Real Fatou Conjecture. (AM-144) UR - http://www.jstor.org/stable/j.ctt7zv8rh.7 Y2 - 2020/10/19/ ER -