Citation Context

...y of being observable in the sense that 1 n P n 1 k=0sT k x ! weakly for all x 2 M except a set of points of Riemannian volume zero. An excellent source for this and related results is Bowen's book [=-=2]-=-. In nonhyperbolic situations the relation between observable measures and equilibrium states is less clear. In the case of piecewise C 2 -maps f : [0; 1] ! [0; 1] Ledrappier [17] proved that an ergod...

Citation Context

...rce for this and related results is Bowen's book [2]. In nonhyperbolic situations the relation between observable measures and equilibrium states is less clear. In the case of piecewise C 2 -maps f : =-=[0-=-; 1] ! [0; 1] Ledrappier [17] proved that an ergodic f-invariant measure with positive Lyapunov exponent () := R log jf 0 j d and Kolmogorov-Sinai entropy h() is absolutely continuous with respect to ...