On Shrinking Targets for Piecewise Expanding Interval Maps

الأصل · EN

For a map T [0,1] → [0,1] with an invariant measure μ, we study, for a μ-typical x, the set of points y such that the inequality |Tⁿ x - y| < rₙ is satisfied for infinitely many n. We give a formula for the Hausdorff dimension of this set, under the assumption that T is piecewise expanding and μϕ is a Gibbs measure. In some cases we also show that the set has a large intersection property.