Box and Hausdorff Dimension of Self-Affine Sets

摘要

Under a natural assumption the Hausdorff dimension of a measure micrometer canonically associated to a given self-affine set is computed. A simplified proof of Bowen's formula for the box dimension of self-affine sets is given. A condition for the box dimension and Hausdorff dimension to be equal is proven and a collection of examples in which this condition can be checked is discussed. (Copyright (c) 1988 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)