Quantitative recurrence properties and homogeneous self-similar sets

2018/01/31 by Chang, Yuanyang, Wu, Min, Wu, Wen · 3 citations
#11K55 #28A80 #28D05 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.10334

Abstract

Let K be a homogeneous self-similar set satisfying the strong separation condition. This paper is concerned with the quantitative recurrence properties of the natural map T: K→ K induced by the shift. Let μ be the natural self-similar measure supported on K. For a positive function φ defined on ℕ, we show that the μ-measure of the following set \beginequation* R(φ):=\x∈ K: |Tⁿ x-x|

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