Science China Mathematics

, Volume 55, Issue 7, pp 1387–1394

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

Authors

  • ChenWei Wang
    • Department of MathematicsNanjing Normal University
    • Department of MathematicsNanjing Normal University
    • Center for Nonlinear ScienceNanjing University
Articles

DOI: 10.1007/s11425-012-4412-0

Cite this article as:
Wang, C. & Chen, E. Sci. China Math. (2012) 55: 1387. doi:10.1007/s11425-012-4412-0

Abstract

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.

Keywords

projection entropyprojection pressureHausdorff dimensionvariational principleBowen’s equation

MSC(2010)

37A4537C45
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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012