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

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

2010-03-12

arxiv.org/abs/1003.2605v1

Mathematics

Dynamical Systems

Scientific paper

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 $\phi\in C(\mathbb{R}^d)$ 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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