a1 Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien
a2 Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900 Heidelberg
We show that equilibrium states μ of a function φ on ([0,1], T), where T is piecewise monotonic, have strong ergodic properties in the following three cases:
(i) sup φ — inf φ <htop(T) and φ is of bounded variation.
(ii) φ satisfies a variation condition and T has a local specification property.
(iii) φ = —log |T′|, which gives an absolutely continuous μ, T is C2, the orbits of the critical points of T are finite, and all periodic orbits of T are uniformly repelling.
(Received February 01 1982)