On the variational principle for the topological pressure for certain non-compact sets  

作　　者：PEI Yu 1 & CHEN ErCai 1,2,1 Department of Mathematics,Nanjing Normal University,Nanjing 210097,China 2 Center for Nonlinear Science,Nanjing University,Nanjing 210093,China 

出　　处：《Science China Mathematics》2010年第4期1117-1128,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10571086);the National Basic Research Program of China (Grant No.2007CB814800)

摘　　要：Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous map.We assume that the dynamical system satisfies g-almost product property and the uniform separation property.We compute the topological pressure of saturated sets under these two conditions.If the uniform separation property does not hold,we compute the topological pressure of the set of generic points.We give an application of these results to multifractal analysis and finally get a conditional variational principle.Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous map.We assume that the dynamical system satisfies g-almost product property and the uniform separation property.We compute the topological pressure of saturated sets under these two conditions.If the uniform separation property does not hold,we compute the topological pressure of the set of generic points.We give an application of these results to multifractal analysis and finally get a conditional variational principle.

关 键 词：uniform separation PROPERTY g-almost product PROPERTY topological pressure of non-compact sets VARIATIONAL principle BS-dinmension 

分 类 号：O189.11[理学—数学]