Science China Mathematics

, Volume 55, Issue 7, pp 1387–1394 | Cite as

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



Let {Si}i=1l 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 φC(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.


projection entropy projection pressure Hausdorff dimension variational principle Bowen’s equation 


37A45 37C45 


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© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsNanjing Normal UniversityNanjingChina
  2. 2.Center for Nonlinear ScienceNanjing UniversityNanjingChina

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