Abstract
The characteristics of cookie-cutter sets in ℝd are investigated. A Bowen's formula for the Hausdorff dimension of a cookie-cutter set in terms of the pressure function is derived. The existence of self-similar measures, conformal measures and Gibbs measures on cookie-cutter sets is proved. The dimension spectrum of each of these measures is analyzed. In addition, the locally uniformly α-dimensional condition and the fractal Plancherel Theorem for these measures are shown. Finally, the existence of order-two density for the Hausdorff measure of a cookie-cutter set is proved.
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