 95251 Howard Weiss
 The Lyapunov and Dimension Spectra of Equilibrium Measures for Conformal
Expanding Maps
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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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