Dimension of self-conformal measures associated to an exponentially
separated analytic IFS on $\mathbb{R}$
Dimension of self-conformal measures associated to an exponentially
separated analytic IFS on $\mathbb{R}$
We extend Hochman's work on exponentially separated self-similar measures on $\mathbb{R}$ to the real analytic setting. More precisely, let $\Phi=\left\{ \varphi_{i}\right\} _{i\in\Lambda}$ be an iterated function system on $I:=[0,1]$ consisting of real analytic contractions, let $p=(p_{i})_{i\in\Lambda}$ be a positive probability vector, and let $\mu$ be the associated self-conformal measure. Suppose …