程崇庆 - 南京大学

个人简介

教授、博导、长江学者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预印本 • Cheng C.Q., Non-existence of KAM torus • Cheng C.Q., Cheng C.Q., Abundance of Arnold duffusion in a priori stable 著作 • 程崇庆，孙义燧：哈密顿系统的有序与无序运动，上海科教出版社 (1996). 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）部分国际会议邀请报告 • 45-minutes invited talk, 26-th International Congress of Mathematicians, 2010 Hyderbad, India • 30-minutes invited talk, 16-th International Congress of Mathematical Physics, August 3-8, 2009, Prague, Czech • One hour invited talk, New Connections between Dynamical Systems and Hamiltonian PDEs, June 1-6, 2009, Maiori, Italy • One hour invited talk, Conference on weak KAM theory, February 1-6, 2009, Nice, France • One hour invited talk, Conference on Stability and Instability in Mechanical Systems, September 22-26, 2008, Barcelona, Spain • Mini-course, Advanced Course on Stability and Instability in Mechanical Systems, September 15-19, 2008, Barcelona, Spain • Mini-course, Hamiltonian dynamical systems and applications, June 18-29, 2007, Montreal, Canada • One-hour invited talk, Conference on Dynamical systems, July 10-16, 2005, Oberwolfach, Germany • 50 minutes invited talk, International Conference on Chaos and Dynamical Complexity, May 16-20, 2005, Hsinchu, Taiwan • One-hour plenary lecture, The 3rd International Congress of Chinese Mathematicians, December 17-24, 2004，Hong Kong • One-hour invited talk, Dynamical Day, University of Paris 7, December 3, 2004, Paris, France • One-hour invited talk, Workshop on Hamiltonian Dynamical Systems, May 24-28, 2004, Montreal, Canada • One-hour invited talk, Conference on Dynamical Systems, July 15-21, 2001, Oberwolfach, Germany • One-hour invited talk, Clay Mathematics Institute Symposium and Euro- Workshop on Hamiltonian Systems, May 21- June 1, 2001, Edinburgh, UK • 45-minute invited talk, The 3rd Asian Mathematical Conference, October 23-27, 2000, Diliman, Philippines • One-hour invited talk, Workshop on the determination of homoclinic trajectories in Hamiltonian systems and Arnold’s diffusion, September 6-17, 1999, IHES, Paris, France • 45-minute invited talk, The 1st International Congress of Chinese Mathematicians, December 12-16, 1998, Beijing

研究领域

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理论与弱KAM理论

近期论文

查看导师新发文章（温馨提示：请注意重名现象，建议点开原文通过作者单位确认）

• Cheng C.Q., Variational construction of diffusion orbits for positive definite Lagrangians, Proceedings of Intnational Congress of Mathematicians vol 3 (2010) 1714-1728. • Cheng C.Q. & Li X., Variational construction of unbounded orbits in Lagrangian systems, Science China: Mathematics 53 (3) (2010) 617-624. • Li X. & Cheng C.Q., Connecting orbits of autonomous Lagrangian systems, Nonlinearity 23 (2010) 119-141. • Cheng C.Q. & Yan J., Arnold diffusion in Hamiltonian Systems: a priori unstable case, J. Differential Geometry, 82 (2009) 229-277. • Cheng C.Q. & Yan J., Variational construction of diffusion orbits in convex Hamiltonian systems with multiple degrees of freedom, Proceedings ICCM’2004, AMS/IP Studies in Advanced Mathematics 42 (2008) 11-27. • Cheng C.Q., Variational methods for the problem of Arnold diffusion, in Hamiltonian Dynamical systems and applications W Craig (ed.) Springer (2008) 337-366. • 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.