Abstract
Let {S i } l i=1 be an iterated function system (IFS) on ℝd with attractor K. Let π be the canonical projection. In this paper, we define a new concept called “projection pressure” P π (φ) for φ ∈ C(ℝd) 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.
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Wang, C., Chen, E. Projection pressure and Bowen’s equation for a class of self-similar fractals with overlap structure. Sci. China Math. 55, 1387–1394 (2012). https://doi.org/10.1007/s11425-012-4412-0
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DOI: https://doi.org/10.1007/s11425-012-4412-0