Let {Si}li=1 be an iterated function system （IFS） 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 ∈（Rd） under cer...Let {Si}li=1 be an iterated function system （IFS） 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 ∈（Rd） under certain arlene 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 Si 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.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10971100)National Basic Research Program of China (973 Program) (Grant No. 2007CB814800)
文摘Let {Si}li=1 be an iterated function system （IFS） 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 ∈（Rd） under certain arlene 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 Si 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.
