an:04040886
Zbl 0638.58021
Nowicki, Tomasz
A positive Lyapunov exponent for the critical value of an \(S\)-unimodal mapping implies uniform hyperbolicity
EN
Ergodic Theory Dyn. Syst. 8, No. 3, 425-435 (1988).
00166514
1988
j
37D20 37A05 28D05
Lyapunov exponent; hyperbolicity
A positive Lyapunov exponent for the critical value of an \(S\)-unimodal mapping implies a positive Lyapunov exponent of the backward orbit of the critical point, uniform hyperbolic structure on the set of periodic points and an exponential diminution of the length of the intervals of monotonicity. This is the proof of the Collet-Eckmann conjecture from 1981 in the general case [\textit{P. Collet} and \textit{J. Eckmann}, Ergodic Theory Dyn. Syst. 3, 13--46 (1983; Zbl 0532.28014)].
T.Nowicki
Zbl 0532.28014