On statistical properties for nonlinear nonhyperbolic systems

非线性非双曲系统的统计特性

基本信息

批准号：
09640289
负责人：
YURI Michiko
金额：
$ 1.34万
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：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640289/
关键词：
Large Deviation Central limit theorem Intermittent system Equilibrium state Variational principle Entropy Nonuniformly hyperbolicity IntermiHent System Namuniformly hyperbolicity indifferent periodic point Decay of correlations Perro

项目摘要

(1997)One of purposes of this project is to establish Large Deviation results for systems without uniformly hyperbolicity. About this problem, I solved it as follows : For piecewise C^1-Bernoulli maps with one indifferent periodicorbits, Large Deviation results for preimages weighted by the derivativeswere established under certain conditions, more precisely, upper boundsin the level 2 Large Deviation Principle <bounded integral>. To solve the problem, Prof.M.Pollicott's visit to Sapporo was meaningful. Further more I could obtain a positive feeling to establish bounds on correlations for nonhyperbolic maps in future. Another purpose of this project is to study asymptotic behavior of ergodic sums, in particuler, convergence to thenormal distributions.About this problem, Prof.M.Denker's visit gave a lot of contributions in solving it. In fact, by his advices I could have a confidenceof importance of my examples and I could establish an extended resultson the central limit theorem which are ajplicable to new nonhyperbolicphenomena. The paper [4] containing the results was submitted to Transaction of the American mathematical Society.(1998)In the second year project, I studied the rates of decay ofcorrelationsfor maps with indifferent perodic points. I could present an approach to estimating the rates by generalizing Liverani's random parturbations of Perron-Frobenius operators which goes back to Bunimovich-Sinai-Chernov's Markov approximation method. The result is contained in [5] which is a joint paper with M.Pollicott.

（1997）该项目的目的之一是为没有均匀双曲线的系统建立较大的偏差结果。关于这个问题，我解决了如下：对于具有一个冷漠周期性的分段c^1-bernoulli地图，在某些条件下建立的衍生品加权的预映射的较大偏差结果，更精确地是在上限的上限，上限为2级的2级大偏差原理<有限的集成>。为了解决这个问题，Pollicott教授对Sapporo的访问是有意义的。此外，我还可以获得积极的感觉，以建立未来非遗传图地图的相关性的界限。该项目的另一个目的是研究千古和在颗粒物中的渐近行为，在当时的正态分布中融合。实际上，通过他的建议，我可能对我的例子有信心，并且可以建立一个扩展的结果，该结果是中心限制定理，这对新的非遗传性苯丙烯瘤而言是可观的。包含结果的论文[4]已提交给美国数学学会的交易。（1998）在第二年项目中，我研究了与perodic perodic点无关的衰减相关图的发生率。我可以通过概括利弗拉尼（Liverani）的perron-frobenius操作员的随机偏置来介绍一种方法来估计费率，该方法可以追溯到Bunimovich-Sinai-Chernov的Markov近似方法。结果包含在[5]中，这是M.pollicott的联合纸。