, Volume 55, Issue 7, pp 1387-1394
Date: 14 May 2012

Projection pressure and Bowen’s equation for a class of self-similar fractals with overlap structure

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Abstract

Let {S i } i=1 l be an iterated function system (IFS) on ℝ d with attractor K. Let π be the canonical projection. In this paper, we define a new concept called “projection pressure” P π (φ) for φC(ℝ d ) under certain affine IFS, and show the variational principle about the projection pressure. Furthermore, we check that the unique zero root of “projection pressure” still satisfies Bowen’s equation when each S i is the similar map with the same compression ratio. Using the root of Bowen’s equation, we can get the Hausdorff dimension of the attractor K.