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The pointwise dimension of self-similar measures

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Chinese Science Bulletin 1999年第23期44卷 2136-2140页

作者： chen ercai and XIONG Jincheng Department of Mathematics , Nanjing Normal University , Nanjing 210097, China Department of Mathematics , South China Normal University, Guangzhou 510631 , China Department of Mathematics Nanjing Normal University Nanjing China Department of Mathematics South China Normal University Guangzhou China

The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist equals the dimenti... 详细信息

关键词： self-similar measure point wise dimension Hausdorff dimension multifractal symbolic space.

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

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Science China Mathematics 2010年第4期53卷 1117-1128页

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 Department of Mathematics Nanjing Normal University Nanjing China Center for Nonlinear Science Nanjing University Nanjing China

Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous *** assume that the dynamical system satisfies g-almost product property and the uniform separation *** compute the topological pressure of saturated sets under these two *** the uniform separation property does not hold,we compute the topological pressure of the set of generic *** 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

Dimension and measure theoretic entropy of a subshift in symbolic space

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Chinese Science Bulletin 1997年第14期42卷 1193-1196页

作者： chen ercai and XIONG Jincheng1. Department of Astronomy, Nanjing University, Nangjing 210093, China 2. Department of Mathematics, South China Normal University, Guangzhou 510631, China Department of Astronomy Nanjing University Nangjing China Department of Mathematics South China Normal University Guangzhou China

1 Definitions and resultsWITH the development of the theory of dynamical systems and fractal geometry, one provedthat symbolic dynamics is a powerful tool to study chaos and fractals. It is useful to study thefractal characteristics of symbolic dynamics. In the present note we shall point out the relationbetween the dimension and measure theoretic entropy of any subshift in symbolic space. Weprove here that the Bowen’s formula for Hausdorff dimension holds without Markov struc-ture. A variational principle for dimension is obtained.

关键词： symbolic space subshift measure theoretic entropy dimension.

THERMODYNAMIC FORMALISM FOR SUBADDITIVE SEQUENCE OF DISCONTINUOUS FUNCTIONS

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Analysis in Theory and Applications 2010年第2期26卷 174-185页

作者： Xianfeng Ma (Nanjing Normal University/East China University of Science and Technology, China) ercai chen (Nanjing Normal University/Nanjing University, China) Yu Pei (Nanjing Normal University, China) School of Mathematics and Computer Science Nanjing Normal Uniersity Nanjing P. R. China Department of Mathematics East China University of Science and Technology Shanghai P. R. China Center of Nonlinear Science Nanjing University Nanjing P. R. China

The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure. As an application, we give an example on systems with nonzero Lyapunov exponents.

关键词： thermodynamic formalism variational principle topological pressure subadditive sequence of functions

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局部熵的高维重分形分析

系统科学与数学 2008年第1期28卷 40-50页

作者：严珍珍陈二才南京师范大学数学与计算机科学学院南京210097 南京邮电大学数理学院南京210003

对不变测度建立了高维形式的重分形分析,即考察与多维参数相关联的重分形分解.利用非紧集或非不变集的高维(q,μ)熵,给出了局部熵的高维重分形谱的一个关系式.

关键词：重分形分析局部熵拓扑熵熵倍增条件

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局部熵的拓扑压重分形谱

数学进展 2014年第3期43卷 445-454页

作者：严珍珍陈二才李雷南京邮电大学理学院南京江苏210003 南京师范大学数学科学学院南京江苏210097

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,*** al.,***.A,1986... 详细信息

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,*** al.,***.A,1986,33(2):1141-1151]的部分结果.

关键词：重分形分析局部熵非紧拓扑压熵倍增条件 (q,μ)-压

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局部回归维数重分形谱的上界估计

南京师大学报（自然科学版） 2011年第1期34卷 29-34页

作者：严珍珍陈二才李雷南京邮电大学理学院江苏南京210003 南京师范大学数学科学学院江苏南京210097

考察局部Poincaré回归时间维数的重分形分解,得到了局部Poincaré回归时间维数的Hausdorff维数重分形谱的上界估计.

关键词：重分形分析回归时间维数 Hausdorff维数 (q τ)-维数

A relative local variational principle for topological pressure

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Science China Mathematics 2010年第6期53卷 1491-1506页

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 Department of Mathematics East China University of Science and Technology Shanghai China School of Mathematics and Computer Science Nanjing Normal University Nanjing China Center of Nonlinear Science Nanjing University Nanjing China College of Mathematics and Physics Nanjing University of Posts and Telecommunications Nanjing China

We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this *** 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 ***,the supremum can be attained by a T-invariant measure.

关键词： pressure conditional entropy relative local variational principle