Zaijiu SHANG

Professor

    Office:

Room 605, Si Yuan Building 

    Telephone:

+86-10-62651277

    E-Mail:

zaijiu@amss.ac.cn
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Research Interests: Hamiltonian systems, Geometric numerical integration, Spectral theory of

                                  differential operators

Research Summary:

  • Develop two general approaches of generating functions for volume-preserving systems and give two  different general ways of constructing volume-preserving integrators for source-free systems (partial results were coauthored with Feng Kang)

  • Give a proper formulation and proof of the existence theorem of KAM (Kolmogorov-Arnold-Moser) invariant tori of symplectic integrators for Hamiltonian systems

  • Give a proof of  the existence theorem of invariant tori with relevant estimates for small twist symplectic mappings in dimensions higher than two

  • Give a complete analytic characterization of J-selfadjoint domains for singular differential operators

Representative Research Works:

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

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

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

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

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

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

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

  • 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.

  • 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.

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

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Institute of Mathematics, AMSS, CAS.    No. 55, Zhongguancun East Road, Beijing 100190, P. R. China  

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