Random covering sets in metric space with exponentially mixing property

Hu, Zhang-nan; Li, Bing

doi:10.1016/j.spl.2020.108922

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2024

Publication Types

Select...

Article3

Other1

Relationship

Self Cite1

Independent3

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They gave a complete characterization of the size E(x) for µ-almost all x. In [17], Hu and Li investigated the dynamical covering sets in (X, B, T, µ, d) with exponentially mixing property, where µ is an Ahlfors s-regular Borel probability measure. They showed that the measure µ(E(x)) is 0 or 1 for µ-a.e.…”

Section: Introductionmentioning

confidence: 99%

On the Intersection of Dynamical Covering Sets with Fractals

Hu¹,

Li²,

Xiao³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Let (X, B, µ, T, d) be a measure-preserving dynamical system with exponentially mixing property, and let µ be an Ahlfors s-regular probability measure. The dynamical covering problem concerns the set E(x) of points which are covered by the orbits of x ∈ X infinitely many times. We prove that the Hausdorff dimension of the intersection of E(x) and any regular fractal G equals dim H G + α − s, where α = dim H E(x) µ-a.e. Moreover, we obtain the packing dimension of E(x) ∩ G and an estimate for dim H (E(x) ∩ G) for any analytic set G.

show abstract

Section: Introductionmentioning

confidence: 99%