Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 807405, 10 pages
http://dx.doi.org/10.1155/2012/807405
Research Article

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

Chenwei Wang1 and Ercai Chen1,2

1School of Mathematics, Nanjing Normal University, Nanjing 210046, China
2Center of Nonlinear Science, Nanjing Normal University, Nanjing 210093, China

Received 1 March 2012; Accepted 15 April 2012

Academic Editor: Francisco Solis

Copyright © 2012 Chenwei Wang and Ercai Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.