A relative local variational principle for topological pressure  

作　　者：MA XianFeng1,CHEN ErCai2,3,& ZHANG AiHua2,4 1Department of Mathematics,East China University of Science and Technology,Shanghai 200237,China 2School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China 3Center of Nonlinear Science,Nanjing University,Nanjing 210093,China 4College of Mathematics and Physics,Nanjing University of Posts and Telecommunications,Nanjing 210046,China 

出　　处：《Science China Mathematics》2010年第6期1491-1506,共16页中国科学：数学（英文版）

基　　金：supported by the Fundamental Research Funds for the Central Universities;Postdoctoral Science Research Program of Jiangsu Province,China (Grant No.0701049C);supported by National Natural Science Foundation of China (Grant No.10971100);supported by National Basic Research Program of China (973 Program) (Grant No.2007CB814800)

摘　　要：We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this pressure.More precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on X.Moreover,the supremum can be attained by a T-invariant measure.We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this pressure.More precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on X.Moreover,the supremum can be attained by a T-invariant measure.

关 键 词：pressure CONDITIONAL entropy RELATIVE LOCAL VARIATIONAL PRINCIPLE 

分 类 号：O189.11[理学—数学]