On the intersection of dynamical covering sets with fractals

摘要

Let ( X, B, mu, T, d) be a measure-preserving dynamical system with exponentially mixing property, and let mu 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 with dimH G > s - alpha equals dimH G + alpha - s, where alpha = dim(H) E(x) mu-a.e. Moreover, we obtain the packing dimension of E(x) boolean AND G and an estimate for dim(H)(E(x) boolean AND G) for any analytic set G.

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