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尚在久

時間:2015-01-16  來源:文本大小:【 |  | 】  【打印

辦公室:N828

電話:010-82541518箱:zaijiu#amss.ac.cn

研究方向:幾何數值方法,哈密爾頓系統,微分算子譜理論

主要成果:

1.   發展了保體積系統的生成函數理論, 給出無源系統保體積算法的一般性構造方法(其中部分成果與馮康合作)

2.   發現計算不變環面時的步長共振現象并給出步長遠離共振的Diophantine條件,證明了Diophantine時間步長集合的大測度性質,證明了辛幾何算法的KAM (Kolmogorov-Arnold-Moser)定理

3.   證明了高維小扭轉辛映射不變環面的存在性(Moser小扭轉定理的高維推廣), 給出辛映射情形KAM定理的完整證明以及有關重要估計

4.   給出奇異常微分算式J-自伴邊界條件的完整解析描述(獲1993年國家教委科技進步二等獎,排名第二)

表論著:

1.   Shang Zaijiu: Stability of symplectic integrators, Preprint 2008.

2.   Shang Zaijiu, Song Lina: Exponentially small splittings of homoclinic orbits of Hamiltonian systems under symplectic discretizations, Preprint 2008.

3.   Shang Zaijiu: Volume-preserving maps, source-free systems and their local structures, Journal of Physics A: Mathematical and General, 39:19 (2006), 5601-561.

4.   Shang Zaijiu: Resonant and Diophantine step sizes in computing invariant tori of Hamiltonian systems. Nonlinearity 13 (2000), 299-308.

5.   Shang Zaijiu: A note on the KAM theorem for symplectic mappings. Journal of Dynamics and Differential Equations 12 (2000), 357-383.

6.   Shang Zaijiu: KAM theorem of symplectic algorithms for Hamiltonian systems. Numerische Mathematik 83 (1999), 477-496.

7.   Feng Kang and Shang Zai-jiu: Volume-preserving algorithms for source-free dynamical systems. Numerische Mathematik 71 (1995), 451-463.

8.   Shang Zaijiu: Generating functions for volume-preserving mappings and Hamilton-Jacobi equations for source-free systems. Science in China (Series A) 37 (1994), 1172-1188.

9.   Shang Zaijiu: On the construction of the volume-preserving difference schemes for source-free systems via generating functions. Journal of Computational Mathematics 12 (1994), 265-272.

10. Shang Zaijiu: On J-selfadjoint extensions of J-symmetric ordinary differential operators. Journal of Differential Equations 73 (1988), 153-177.

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