an:01270128
Zbl 0916.58020
Bruin, Henk; Keller, Gerhard
Equilibrium states for \(S\)-unimodal maps
EN
Ergodic Theory Dyn. Syst. 18, No. 4, 765-789 (1998).
00054952
1998
j
37D20 37D35
\(S\)-unimodal map; equilibrium state; uniformly hyperbolic; logistic map; pressure function
The authors study for \(S\)-unimodal maps \(f\) equilibrium states maximizing the free energies \(F_t(\mu):= h(\mu)+ t\int\log| f'| d\mu\) and the pressure function \(P(t):= \sup_\mu F_t(\mu)\). It is shown that if \(f\) is uniformly hyperbolic on periodic orbits, then \(P(t)\) is analytic for \(t\approx 1\). Morover, the authors investigate the stability of \(F_t\) for a large class of functions but also give an example of a logistic map that is not stable and has no equilibrium state.
Messoud Efendiev (Berlin)