Mathematical characterization of chaotic itinerancy

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610034
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Hitotsubashi University
• Principal Investigator: SAIKI YOSHITAKA 一橋大学, 大学院商学研究科, 准教授 (20433740)
• Research Collaborator: ESASHI Kunihiko ; ONOZAKI Tamotsu ; KOBAYASHI Miki U ; SATO Yuzuru ; YAMADA Michio ; Chian Abraham C.-L. ; Das Suddhasattwa ; Dock Chris B. ; Miranda Rodrigo A. ; Salgado-Flores Martin ; Rempel Erico L. ; Sander Evelyn ; Wu Jin ; Yorke James A.
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 力学系 / 数値解析 / 応用数学 / 複雑現象の数理

Outline of Final Research Achievements

Chaotic itinerancy is know as "Complex phenomena wandering among multi chaotic states irregularly", but does not have a certain mathematical characterization. We analyze a dynamics of a minimal model having the inevitable properties to be chaotic itinerancy. One of the models we studied was a two-dimensional torus map showing intermittency. It is expanding in x-direction and expanding or contracting in y-direction depending on the x value. We find that behind the dynamics exist the coexistence of repellers and saddles and quasi-periodic orbits. Through this study we develop a technique for calculating the Birkhoff average along a quasiperiodic orbit.

Free Research Field

力学系、応用数学