Projection Pressure and Bowen's Equation for a Class of Self-similar Fractals with Overlap Structure

Chenwei Wang; Ercai Chen

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arXiv · 1003.2605

Projection Pressure and Bowen's Equation for a Class of Self-similar 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 $\mathbb{R}^d$ with attractor K. Let $π$ be the canonical projection. In this paper we define a new concept called "projection pressure" $P_π(ϕ)$ for $ϕ\in C(\mathbb{R}^d)$ 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 $K$.

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Chenwei Wang, Ercai Chen. 2010-03-12. Projection Pressure and Bowen's Equation for a Class of Self-similar Fractals with Overlap Structure. https://arxiv.org/abs/1003.2605

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