On statistical properties for nonlinear nonhyperbolic systems
Project/Area Number  09640289 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Sapporo University 
Principal Investigator 
YURI Michiko Sapporo University, Department of Business Administration, Professor, 経営学部, 教授 (70174836)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1998 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1997 : ¥1,200,000 (Direct Cost : ¥1,200,000)

Keywords  Large Deviation / Central limit theorem / Intermittent system / Equilibrium state / Variational principle / Entropy / Nonuniformly hyperbolicity / IntermiHent System / Namuniformly hyperbolicity / indifferent periodic point / Decay of correlations / PerrowFroberius operator / congormal measure / Variational Principle / Noruniformly hyperbolicity 
Research Abstract 
(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^1Bernoulli 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 PerronFrobenius operators which goes back to BunimovichSinaiChernov's Markov approximation method. The result is contained in [5] which is a joint paper with M.Pollicott. 区分的に可逆なindifferent periodic pointを有した多次元系に対して、時間相関関数の減少のオーダーを評価することができた。〔参照(5)〕

Report
(4results)
Research Output
(18results)