Projection pressure and Bowen’s equation for a class of selfsimilar fractals with overlap structure
 ChenWei Wang,
 ErCai Chen
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Abstract
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 φ ∈ C(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.
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 Title
 Projection pressure and Bowen’s equation for a class of selfsimilar fractals with overlap structure
 Journal

Science China Mathematics
Volume 55, Issue 7 , pp 13871394
 Cover Date
 20120701
 DOI
 10.1007/s1142501244120
 Print ISSN
 16747283
 Online ISSN
 18691862
 Publisher
 SP Science China Press
 Additional Links
 Topics
 Keywords

 projection entropy
 projection pressure
 Hausdorff dimension
 variational principle
 Bowen’s equation
 37A45
 37C45
 Authors

 ChenWei Wang ^{(1)}
 ErCai Chen ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China
 2. Center for Nonlinear Science, Nanjing University, Nanjing, 210093, China