95-251 Howard Weiss

The Lyapunov and Dimension Spectra of Equilibrium Measures for Conformal Expanding Maps (27K, TeX) Jun 5, 95

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Abstract. In this note, we find an explicit relationship between the dimension spectrum for equilibrium measures and the Lyapunov spectrum for conformal repellers. We explicitly compute the Lyapunov spectrum and show that it is a delta function. We observe that while the Lyapunov exponent exists for almost every point with respect to an ergodic measure, the set of points for which the Lyapunov exponent does not exist has positive Hausdorff dimension if the SRB measure does not coincide with the measure of maximal entropy. It follows that for such conformal repellers, the set of points for which the pointwise dimension of the measure of maximal entropy does not exist has positive Hausdorff dimension.

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