Characteristics of weak chaos in view of large deviation analysis and infinite ergodicity

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400411
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Waseda University
• Principal Investigator: Aizawa Yoji 早稲田大学, 理工学術院, 名誉教授 (70088855)
• Co-Investigator(Renkei-kenkyūsha): TSUGAWA Satoru 早稲田大学, 理工学術院, 助手 (20607600) ; NAKAGAWA Masaki 早稲田大学, 理工学術院, 助手 (80649202)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 非線形力学系 / カオス理論 / 近可積分ハミルトン系 / 無限エルゴード性 / 非カオス的ストレンジアトラクター / 光乱流現象 / 生物の群れの集団運動 / 地震統計法則

Outline of Final Research Achievements

There still remain many unsolved problems in the nonstationary regime of chaotic or turbulent phenomena; for instance, anomalous diffusion in hamiltonian systems, intermittency, and infinite ergodicity, et cetera. In this research, we studied several nonlinear dynamical models, such as the hamiltonian dynamics of lattice vibrations, mushroom billiards with clear boundaries between chaos and torus, antlion models with dissipative infinite measure ergodicity, nonchaotic strange attractors in periodically driven systems, wave turbulence in Bloch equation, etc., and succeeded to elucidate the diversity of the nonstationary chaos and its universal aspects in statistical behaviors.　Furthermore, we studied a new method for the numerical analysis of chaotic intermittent time series by using the real data of interoccurrence time statistics of earthquakes, and succeeded to obtain some new statistical laws of magnitude correlations in the shock sequences.

Free Research Field

物理学