2012 Fiscal Year Final Research Report
Bifurcations and Homo- and Heteroclinic Behavior in Infinite- Dimensional Dynamical Systems
| Project/Area Number |
21540124
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hiroshima University (2012)
Niigata University (2009-2011) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
ITO Hidekazu 金沢大学, 数物科学系, 教授 (90159905)
SHIBAYAMA Mitsuru 大阪大学, 大学院・基礎工学研究科, 講師 (40467444)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 力学系 / 無限次元系 / 分岐 / ホモ/ヘテロクリニック挙動 / 摂動法 / 微分ガロア理論 / 数値解析 |
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| Research Abstract |
Bifurcations and homo- and heteroclinic motions in several infinite-dimensional dynamical systems such as partial differential equations and discrete lattices were studied. In particular, perturbation methods to obtain conditions for saddle-node and pitchfork bifurcations of homo- and heteroclinic orbits in ordinary differential equations, which correspond to soliton, pulse and front solutions in partial differential equations, were developed, and their relationship with the integrability of variational equations around these orbits in the meaning of differential Galois theory was
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