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年）该项目的目的之一是阐明足够的条件，以实现可计数的共形测量值，以使一个分段可逆的马尔可夫系统。关于这个问题，M.Denker教授在萨波罗期间提供了宝贵的建议，以便我可以建立一种新方法来构建保形测量，该方法基于衍生的地图T^*（Schweiger的跳跃转换）的存在，该方法均匀地扩展并保证了弱的电位φ^*与共相匹配的弱持有人型属性。结果包含在（3）中，该纸是M.Denker的联合纸。该项目的另一个目的是建立有关具有无关定期点的非可逆地图的相关函数衰减的界限。我可以通过基于perron-frobenius oberators的随机部分应用Liverani的方法来获得多项式界限，并估算（1）中建立的不变周期性点附近不变密度的差异顺序。结果包含在（4）中，这是与M.Pollicott的联合论文。（2000）在第二年项目中，我研究了动态ZETA函数的Meromorormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormorphic函数，用于具有漠不关心的周期点。我可以通过观察φ的拓扑压力与与跳转转换T^*相关的φ^*相关的拓扑压力之间的良好关系来阐明Zeta函数的Meromororphic Dmeain。结果包含在（5）中，该纸是M.pollicott的联合纸。此外，我可以通过在紧凑型集合上以不包括漠不关心的周期性点（不包括周期性点）的速度来提高（4）中（4）中相关性衰减率的结果。结果包含在（6）中。