Projection pressure and Bowen’s equation for a class of self-similar fractals with overlap structure |
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Authors: | ChenWei Wang ErCai Chen |
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Institution: | 1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China 2. Center for Nonlinear Science, Nanjing University, Nanjing, 210093, China
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Abstract: | Let {Si}il=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" Pπ(φ) for ∈ 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 Si 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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Keywords: | projection entropy projection pressure Hausdorff dimension variational principle Bowen’s equation |
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