Statistical properties of equilibrium states for complex systems

复杂系统平衡状态的统计特性

基本信息

批准号：
11640134
负责人：
YURI Michiko
金额：
$ 1.6万
依托单位：
Sapporo University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640134/
关键词：
Indifferent periodic points Intermittency Decay of correlations Equilibrium state Perron-Frobenius operator Zeta function Variational principle Weak Gibbs measure Decay of Correlations Meromorphic extension Conformal measure Indiffer

项目摘要

(1999)One of purposes of the project in 1999 is to clarify sufficient conditions for the existence of conformal measures for countable to one piecewise invertible Markov systems. About this problem, Prof.M.Denker gave valuable advices during his stay in Sapporo so that I could establish a new method for the construction of conformal measures which is based on the existence of a derived map T^* (Schweiger's jump transformation) which is uniformly expanding and guarantees a weak Holder-type property of the potential φ^* associated to φ. The result is contained in (3) which is a joint paper with M.Denker. Another purpose of the project is to establish bounds on decay of correlation functions for noninvertible maps with indifferent periodic points. I could obtained polynomial bounds by applying Liverani's method based on random parturbations of Perron-Frobenius operators and by estimating order of divergence of invariant densities near indifferent periodic points which was established in (1). The result is containaed in (4) which is a joint paper with M.Pollicott.(2000)In the second year project, I studied meromorphic properties of dynamical zeta functions for noninvertible maps with indifferent periodic points. I could clarify the meromorpic dmeain of the zeta functions by observing a good relation between the topological pressure for φ and the topological pressure associated to φ^* with respect to the jump transformation T^*. The result is contained in (5) which is a joint paper with M.Pollicott. Furthermore, I could improve the results on the rates of decay of correlations in (4) by clarifying the speed of uniform convergence of iterated Perron-Frobenius operators on compact sets excluding indifferent periodic points. The result is contained in (6).

(1999) 1999年该项目的目的之一是阐明可数分段可逆马尔可夫系统保形测度存在的充分条件，M.Denker教授在札幌逗留期间对此问题提出了宝贵的建议。我可以建立一种新的共形测度构造方法，该方法基于导出映射 T^*（施威格跳跃变换）的存在，该映射均匀扩展并保证弱与 φ 相关的势 φ^* 的持有者类型属性结果包含在与 M.Denker 的联合论文中。该项目的另一个目的是建立不可逆映射的相关函数衰减的界限。我可以通过应用基于 Perron-Frobenius 算子的随机parturbations的Liverani方法并通过估计无差异周期点附近的不变密度的散度阶来获得多项式界限。 (1) 中建立的点的结果包含在 (4) 中，这是与 M.Pollicott 的联合论文。(2000) 在第二年的项目中，我研究了具有无差异周期的不可逆映射的动态 zeta 函数的亚纯性质。我可以通过观察 φ 的拓扑压力和与 φ^* 相关的拓扑压力之间的良好关系来阐明 zeta 函数的亚形态特征。跳跃变换 T^* 的结果包含在（5）中，这是与 M.Pollicott 的联合论文。此外，我可以通过阐明均匀收敛的速度来改进（4）中相关性衰减率的结果。在排除无关周期点的紧集上迭代 Perron-Frobenius 算子结果包含在 (6) 中。