The Projection Pressure for Asymptotically Weak Separation Condition and Bowen's Equation

Abstract EN

Let {Si}i=1l be a weakly conformal iterated function system on Rd with attractor K.

Let π be the canonical projection.

In this paper we define a new concept called “projection pressure” Pπ(φ) for φ∈C(Σ) and show the variational principle about the projection pressure under AWSC.

Furthermore, we check that the zero of “projection pressure” still satisfies Bowen's equation.

Using the root of Bowen's equation, we can get the Hausdorff dimension of the attractor K.