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

2010/03/12 by Chenwei Wang, Wang, Chenwei, Ercai Chen +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1003.2605

arxiv created 2010/03/12 · arxiv updated 2010/03/15

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.

Related

• An explicit formula for the pressure of box-like affine iterated\n function systems
• Projections of self-similar and related fractals: a survey of recent developments
• The canonical projection associated with a mixed possibly infinite iterated function system
• Inhomogeneous attractors and box dimension
• Properties of IFS attractors with non-empty interiors, related rough domains, and associated function spaces and scattering problems