Science China Mathematics

, Volume 55, Issue 7, pp 1387-1394

First online:

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

  • ChenWei WangAffiliated withDepartment of Mathematics, Nanjing Normal University
  • , ErCai ChenAffiliated withDepartment of Mathematics, Nanjing Normal UniversityCenter for Nonlinear Science, Nanjing University Email author 

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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.


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


37A45 37C45