2016 Fiscal Year Final Research Report
Mathematical characterization of chaotic itinerancy
Project/Area Number |
26610034
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Foundations of mathematics/Applied mathematics
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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
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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.
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Free Research Field |
力学系、応用数学
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