伯克霍夫平均的压谱(英文)  

Pressure Spectrum for Birkhoff Averages

作　　者：王琛玮[1] 黄萍[2] 

机构地区：[1]南京师范大学数学科学学院,江苏南京210046 [2]解放军理工大学理学院,江苏南京211101

出　　处：《南京师大学报（自然科学版）》2012年第2期8-15,共8页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：Supported by the National Natural Science Foundation of China(10971100)

摘　　要：Legendre变换的作用是将一个独立参变量函数转化为一个新的独立参变量函数.本文证明了在热力学形式中压谱可以由函数T:R→R的Legendre变换所获得.所考虑的函数T为连续可微.用这种方法我们将重分形的问题转化为热力学问题,这些结果对更广一类的可测函数仍成立,包含了(而不仅限于)连续函数.The strategy behind the use of Legendre transforms is to shift, from a function with one of its parameters an in- dependent variable, to a new function with its dependence on a new variable. In this paper, we show that pressure spec- tra may be obtained as Legendre transforms of functions T： R→R arising in the thermodynamic formalism. The primary hypothesis we require is that the functions T be continuously differentiable. In this way we make rigorous the general par- adigm of reducing questions regarding the muhifractal formalism to questions regarding the thermodynamic formalism. These results hold for a broad class of measurable potentials, which includes （but is not limited to） continuous func- tions.

关 键 词：重分形 谱 伯克霍夫 压 

分 类 号：O189[理学—数学]