For an exponentially separated real analytic IFS without a common fixed point, every self-conformal measure has dimension equal to min{1, entropy divided by Lyapunov exponent}.
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Dimension of self-conformal measures associated to an exponentially separated analytic IFS on $\mathbb{R}$
For an exponentially separated real analytic IFS without a common fixed point, every self-conformal measure has dimension equal to min{1, entropy divided by Lyapunov exponent}.