2009 Fiscal Year Final Research Report
Numerical verifications for homo/heteroclinic orbits and their applications to partial differential equations
| Project/Area Number |
19740050
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hiroshima University |
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Principal Investigator |
HIRAOKA Yasuaki Hiroshima University, 大学院・理学研究科, 准教授 (10432709)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 力学系 / 精度保証付き数値計算 / ホモ / ヘテロクリニック軌道 / メルニコフ積分 |
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| Research Abstract |
The purpose of this research is to present fast algorithms to prove existence of homoclinic or heteroclinic orbits appearing dynamical systems by means of computers. The main result obtained in the research period is that we succeeded in showing reasonably fast algorithms to prove existence of homoclinic orbits in reversible dynamical systems. The key idea of this algorithm is to rigorously estimate Melnikov type integrals by computers. On the other hand, when we remove the assumption of reversibility, it does not yet succeeded in obtaining a good algorithm for this purpose.
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Research Products
(7 results)
