Large deviation principle and multifractal analysis in dynamical systems

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540212
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Hiroshima University
• Principal Investigator: Chung Yong Moo 広島大学, 工学(系)研究科(研究院), 准教授 (20314734)
• Co-Investigator(Renkei-kenkyūsha): TAKAHASI Hiroki 慶應義塾大学, 理工学部, 准教授 (00467440) ; SUMI Naoya 熊本大学, 自然科学研究科, 教授 (50301411) ; MIKAMI Toshio 津田塾大学, 学芸学部, 教授 (70229657)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 力学系 / 大偏差原理 / マルチフラクタル

Outline of Final Research Achievements

We obtained a criterion to hold the large deviation principle for smooth dynamical systems on the interval. If a multimodal map without flat critical points has the following properties: (1) the exponential growth of the derivative on the set of critical values with respect to the time evolution; (2) the sub-exponential slow recurrence of the critical orbits; (3) the topological exactness, the large deviation principle of level 2 holds. From our result it is shown that almost every stochastic quadratic map satisfies the large deviation principle. Moreover we gave a representation of the Birkhoff spectrum by using thermodynamic formalism, and showed its continuity.

Free Research Field

力学系理論