牛顿迭代与隐函数定理的应用
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  资源类型 学术讲座
  关 键 词 牛顿迭代 隐函数定理
  更新时间 2009年4月24日
  资源简介 用大量实例解释并学习了牛顿迭代与隐函数定理,并从基本的牛顿迭代法及隐函数定理带领大家理解非线性偏微方程的一些基本问题
 教师姓名 程崇庆
 性    别
 职    称 教授
 所在院系 理学院数学系
 电子邮箱 tres@nju.edu.cn
 联系电话 暂无
 通讯地址 南京大学数学院
  教师简介 程崇庆
南京大学长江特聘教授 (基础数学)
南京大学副校长兼研究生院院长

研究兴趣

Hamilton动力系统:动力学不稳定性,连接轨道的变分构造,Arnold扩散,KAM理论

数学论文
• Cheng C.Q., Hamiltonian systems: stable or unstable? Milan J. Math . 74 (2006) 295-312.

• Zheng Y. & Cheng C.Q., Homoclinic orbits of positive definite Lagrangian systems, J. Differential Equations , 229 (2006) 297-316.

• Cheng C.Q., Minimal invariant tori in the resonant regions of nearly integrable Hamiltonian systems, Transactions of American Mathematical Society 357 ( 12 ) (2005) 5067-5095.

• Cui X.J., Cheng C.Q. & Cheng W., Existence of infinitely many homoclinic orbits to Aubry sets for positive definite Lagrangian systems, J. Differential Equations , 214 (2005) 176-188.

• Cheng C.Q. & Yan J., Existence of diffusion orbits in a priori unstable Hamiltonian systems, J. Differential Geometry , 67 (2004) 457-517.

• Cheng C.Q., KAM 理论与 Arnold 扩散: Hamilton 系统的动力学稳定性问题;中国科学, 34 卷第 3 期( 2004 ) 257-267.

• Yan J. & Cheng C.Q., Dynamics around minimal hyperbolic torus in Hamiltonian systems , Int. J. Mod. Phys. (B) 17 (2003) 3950-3963.

• Cheng W. & Cheng C.Q., Connecting orbits among Denjoy minimal sets for monotone twist map. Science in China 46 (2003) 159-168.

• 王乾,程崇庆:退化情形下高余维双曲不变环面的存在性,中国科学, 32 卷 7 期,( 2002 ) 640-649.

• Cheng C.Q., A KAM theory for resonant tori and a generalization of Poincare Birkhoff fixed point theorem. AMS/IP Studies in Advanced Mathematics 20 (2001) 397-401.

• Cheng C.Q. & Cheng J., Dynamical stability of Hamiltonian systems, Progress in Natural Science 10 (2000) 343-349.

• Cheng W. & Cheng C.Q., Existence of infinitely many non-Birkhoff periodic orbits in twist maps, Science in China 43 (2000) 810-817.

• Cheng W. & Cheng C.Q., On the connecting orbits among local minimizers for monotone twist map, Progress in Nonlinear Analysis 6 World Scientific (2000) 58-80.

• Cheng C.Q., Lower dimensional invariant tori in the regions of instability for nearly integrable Hamiltonian systems, Commun. Math. Phys. 203 (1999) 385-419.

• Cheng C.Q. & Wang S.L., The surviving of lower dimensional tori from resonance torus of Hamiltonian systems, J. Diff. Eqns. 155 (1999) 311-326.

• Cheng C.Q. & Xia Z., KAM theory without the twist condition, Dynamical Systems - The Memorial Volume of Liao S.T., World Scientific (1999) 16-22.

• Wang S.L. & Cheng C.Q., Lower dimensional tori for generic Hamiltonian systems Chinese Science Bulletin 44 (1999) 1187-1191.

• Qian S. & Cheng C.Q., Infinitely many elliptic periodic orbits in higher dimensional symplectic diffeomorphisms, Northeastern Math. J. 15 (1999) 495-502.

• Qin Y. & Cheng C.Q., The non-monotone twist maps and basic hyperbolic sets, Science in China 41 (1998) 1176-1183.

• Wang S.L. & Cheng C.Q., Birkhoff lower dimensional tori in Hamiltonian systems, Chinese Science Bulletin 42 (1997) 1866-1870.

• Cheng C.Q., Birkhoff-Kolmogorov-Arnold-Moser tori in convex Hamiltonian systems, Commun. Math. Phys. 177 (1996) 529-559.

• Cheng C.Q. & Kupper T., Dynamical behavior of two soliton solutions exhibited by perturbed sine-Gordon equation, Math. Nachr. 171 (1995) 53-77.

• Cheng C.Q. & Sun Y.S., Existence of KAM tori in degenerate Hamiltonian systems, J. Diff. Eqns. 114 (1994) 288-335.

• Cheng C.Q., Bifurcations of vector fields with Z4 symmetry, Dynamical systems and Related Topics, 9 (1992) 61-64.

• Cheng C.Q., Metamorphoses of phase portrait of vector fields in the case of symmetry of order 4, J. Diff. Eqns. 95 (1992) 130-139.

• Cheng C.Q., Invariant torus bifurcation series and evolution of chaos exhibited by a forced nonlinear vibration system, Int. J. Nonlinear Mech. 26 (1991) 105-116.

• Cheng C.Q., Hopf bifurcations in non-autonomous systems at points of resonance, Science in China 33 (1990) 206-219.

• Cheng C.Q., & Sun Y.S., Existence of invariant tori in three dimensional measure-preserving mappings, Celestial Mechanics and Dynamical Astronomy 45 (1989/1990) 275-292.

• Cheng C.Q., & Sun Y.S., Existence of periodically invariant curves in three dimensional measure-preserving mappings, Celestial Mechanics and Dynamical Astronomy 45 (1989/1990) 293-303.

• Cheng C.Q., A Hopf-Landau bifurcation series discovered in a nonlinear vibration system, Chinese Science Bulletin 34 (1989) 1169-1172.

• Cheng C.Q., Hopf bifurcation at resonance in non-autonomous systems, Appl. Math. Mech. 10 (1989) 443-453.

• Cheng C.Q., Hopf-Landau bifurcation into higher dimensional tori. Appl. Math. Mech. 10 (1989) 553-562.

• Cheng C.Q., Hopf-Landau bifurcation into higher dimensional tori, Proc. Int. Conf. Bifu. Th. & Numer. Anal. (1988) 134-144.

• Cheng C.Q., On the convergence of substructure synthesis, Proc. Int. Conf. Vibration Problems in Engineering (1986) 245-251.

• Cheng C.Q., On the decoupling problem of equation of motion in the case of complex mode (in Chinese with English summery) J. Nanjing Institute of Tech. (1983) No.4 98-105.

预印本

• Cheng C.Q. & Yan J., Arnold diffusion in Hamiltonian Systems: a priori unstable case.

• Cheng C.Q., Instability of Hamiltonian Systems with Many Degrees of Freedom

获得学术奖励

2001 年 国家自然科学二等奖 ( 第一完成人 )

2000 年 中国高校自然科学一等奖 ( 第一完成人 )

1998 年 首届 Morningside 数学奖(银奖)

1997 年 香港求是杰出青年学者奖(数学)

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