局部熵的拓扑压重分形谱  

Multifractal Spectrum of Topological Pressure for Local Entropies

作　　者：严珍珍[1] 陈二才[2] 李雷[1] 

机构地区：[1]南京邮电大学理学院,南京江苏210003 [2]南京师范大学数学科学学院,南京江苏210097

出　　处：《数学进展》2014年第3期445-454,共10页Advances in Mathematics（China）

基　　金：国家自然科学基金资助项目(No.61070234;No.61179027)

摘　　要：本文考察不变测度的局部熵的重分形分析.给出了集合的非紧拓扑压和非紧(q,μ)-压的定义,并建立了二者之间的联系.利用非紧集或非不变集的(q,μ)-压,给出了局部熵的拓扑压重分形谱的一个等式.此结论推广了文献[Halsey,T.et al.,Phys.Rev.A,1986,33(2):1141-1151]的部分结果.This paper discusses the problem of multifractal analysis of local entropies for any invariant measures. The definitions of topological pressure and （q,μ）-pressure for non- compact or non-invariant sets are given. The relationship between topological pressure and （q, μ）- pressure is established. By using the （q, μ）-pressure of non-compact or non-invariant sets, the equation related with multifractal spectrum of topological pressure for local entopies is obtained. The equation is the generation of part of conclusions of reference [Halsey, T. et al., Phys. Rev. A, 1986, 33（2）： 1141-1151].

关 键 词：重分形分析 局部熵 非紧拓扑压 熵倍增条件 (q μ)-压 

分 类 号：O189.3[理学—数学]