Shrinking target problem for random iterated function systems

Abstract

We describe the shrinking target problem for random iterated function systems which semi-conjugate to a random subshifts of finite type. We get the Hausdorff dimension of the set based on shrinking target problems with given targets. The main idea is an extension of ubiquity theorem which plays an important role to get the lower bound of the dimension. Our method can be used to deal with the sets with respect to an more general targets and the sets based on the quantitative Poincaré recurrence properties.

References in corpus (2)

• The dynamical Borel-Cantelli lemma and the waiting time problems
• Multifractal formalism for inverse measures of random weak Gibbs measures