Shrinking target problem for random iterated function systems

2017/07/05 by Zhihui Yuan, Yuan, Zhihui
Biochemistry, Genetics and Molecular Biology · Mathematics · #11K55 #28A80 #37C45 #37Hxx #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1707.01306

openalex publication_date 2017/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

Related

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• Hausdorff dimension of shrinking targets on Przytycki-Urbański fractals
• Path-dependent shrinking targets in generic affine iterated function systems
• Hausdorff dimension of the set of eventually always hitting points on a self-conformal set
• Shrinking Targets for Countable Markov Maps