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Projection Pressure and Bowen's Equation for a Class of Self-similar Fractals with Overlap Structure | | Chenwei Wang
; Ercai Chen
; | | Date: |
12 Mar 2010 | | Abstract: | Let ${S_i}_{i=1}^{l}$ be an iterated function system(IFS) on $mathbb{R}^d$
with attractor K. Let $pi$ be the canonical projection. In this paper we
define a new concept called "projection pressure" $P_pi(phi)$ for $phiin
C(mathbb{R}^d)$ 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 $K$. | | Source: | arXiv, 1003.2605 | | Services: | Forum | Review | PDF | Favorites | |
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