A multifractal mass transference principle for Gibbs measures with applications to dynamical Diophantine approximation

@inproceedings{Fan2013AMM,
  title={A multifractal mass transference principle for Gibbs measures with applications to dynamical Diophantine approximation},
  author={Ai-Hua Fan and J{\"o}rg Schmeling and Serge Troubetzkoy},
  year={2013}
}
Let mu be a Gibbs measure of the doubling map T of the circle. For a mu-generic point x and a given sequence {r(n)} subset of R+, consider the intervals (T-n x - r(n) (mod 1), T-n x + r(n) (mod 1)). In analogy to the classical Dvoretzky covering of the circle, we study the covering properties of this sequence of intervals. This study is closely related to the local entropy function of the Gibbs measure and to hitting times for moving targets. A mass transference principle is obtained for Gibbs… CONTINUE READING
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