Projection pressure and Bowen's equation for a class of self-similar fractals with overlap structure  

作　　者：WANGChen Wei CHENErCai 

机构地区：[1]Schoo—lofMathematicsSciences,NanjingNormalUniversity,Nanjing210046,China [2]CenterforNonlinearScience,NanjingUniversity,Nanjing210093,China

出　　处：《Science China Mathematics》2012年第7期1387-1394,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10971100);National Basic Research Program of China (973 Program) (Grant No. 2007CB814800)

摘　　要：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.Let {Si}il=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 ∈ C(Rd) 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 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.

关 键 词：projection entropy projection pressure Hausdorff dimension variational principle Bowen＇s equa-tion 

分 类 号：TP212[自动化与计算机技术—检测技术与自动化装置] O153.4[自动化与计算机技术—控制科学与工程]