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| 研究生： |
葉宇軒 Yek, Yu-Hsieh |
|---|---|
| 論文名稱： |
The Poincare-Birkhoff theorem and some of its application 有關Poincare-Birkhoff定理及其應用 |
| 指導教授： |
陳國璋
Chen, Kuo-Chang |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2010 |
| 畢業學年度： | 98 |
| 語文別： | 英文 |
| 論文頁數： | 18 |
| 中文關鍵詞： | Poincare-Birkhoff定理 、固定點 |
| 外文關鍵詞： | Poincare-Birkhoff theorem, twist map |
| 相關次數： | 點閱：68 下載：0 |
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In this article we investigate various versions of
the Poincare-Birkhoff theorem
and briefly describe its history.
We present detailed proof for a generalization by J. Frank.
We also study some applications of the Poincare-Birkhoff theorem to differential equations.
[1] G.D.Birkho , An extension of Poincare's last geometric theorem, Acta math. 47(1925),297-311
[2] W.Y.Ding, A Generalization Of The Poincare-Birkho Theorem, Proc.Am.Math Soc. 88(1983),341-346.
[3] J.Franks, Generalizations of the Poincare-Birkho theorem, Ann.Math. 128(1988),139-151.
[4] J.Franks, Recurrence and xed points of surface homeomorphisms, Ergod.Th.& Dynam.Sys. 8(1988),99-107 .
[5] P.Hartman, On boundary value problems for superlinear second order differential equation, J.Di .Eqns 23(1977),37-53.
[6] H.Jacobowitz, periodic solutions of x''+ f(t,x) = 0 via the Poincare-Birkhoff Theorem, J.Diff.Eqns 20(1976),37-52.
[7] A.Margheri, C.Rebelo and F.Zanolin, Maslov index, Poincare-Birkhoff theorem and periodic solutions of asymptotically linear planar hamiltonian systems, J.Di .Eqns 183(2002),342-367.
[8] C.Zanini, Rotation numbers, eigenvalues and the Poincare-Birkho theorem,J.Math.Anal.Appl. 279(2003), 290-307.
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