研究领域

常微分方程分支理论(正规形理论), 等变动力系统(即具有对称性的动力系统), 非线性科学(混沌), 经济与金融中的非线性问题， 计算机符号计算, 周期解, 人工神经网络等

论著

书 NORMAL FORMS AND BIFURCATION OF PLANAR VECTOR FIELD (WITH S.N.CHOW AND C.LI), CHAMBRIDGE UNIVERSITY PRESS, 1994.

论文

1)周期扰动的非保守系统的周期解, 数学学报, 26:3 (1983), 341-353.

2)关于微分方程 的 周期解的存在性, 数学年刊, 5A(1)(1984), 61-72.

3)On the existence of -periodic solutions of differential equation , in Proceedings of the 1983 Beijing Symposium on Differential Geometry and Differential Equations (1986), S.Liao ed. Science Press.

4)On the monotonicity of the period function of (with S.N.Chow), Casopis pro pestov matematiky, roc. 111(1) (1986), 14-25.

5)Normal forms of bifurcating periodic orbits(with S.N.Chow), Contemporary Mathematics, Vol.56(1986), 9-18.

6)Ph.D thesis, On the monotonicity and critical points of the period functions of some second order equations, Michigan State University, U.S.A., 1986.

7)The critical points of the period function of , Nonlinear Analysis, 11:9 (1987), 1029-1050.

8)Uniqueness of periodic orbits of some vector field with codimension two singularities(with S.N. Chow and C.Li), J.Diff.Equs. 77:2(1989), 231-253.

9)A simple proof on uniqueness of periodic orbits in the 1:3 resonance problem(with S.N.Chow and C.Li), Proc. Ame. Math. Soc. 105:4(1989), 1025-1032.

10)Adjoint operator method in the normal form theory of nonlinear Hamiltonian systems, in Proceedings of the international conference on bifurcation theory and its numerical analysis, Xi'an(1988), eds. Li Kaitai, J.Marsden, M.Golubitsky, G.Iooss, 429-436.

11)An introduction to the normal form theory of ordinary differential equations, (Chinese)Advanced in Math., 19:1 (1990), 38-71.

12)Computation of normal forms(with S.N.Chow and B.Drachman), J. Comp. and Appl. Math., 29:2(1990), 129-143.

13)规范形理论 sl(2,R) 表示论方法的一些新结果, 中国科学 A 辑, 1990年第4期, 343-352.

14)Applications of the representation theory of sl(2,R) to normal form theory, Science in China(ser. A), 33:8(1990), 923-933.

15)Hopf bifurcation at nonzero foci in 1:4 resonance, Acta Math. Sinica, new series, 6:1(1990), 10-17.

16) On limit cycles of continuous Hopfield neural network (with T.Li and W.Jin), in International Symposium on nonlinear problems in engineering and science-numerical and analytical approach(1991), eds.S.Xiao et al. 241-245, Science Press of China, 1992.

17) Hopf bifurcation of continuous Hopfield neural networks consisting of three neurons, in Proc.Inter.Neu.Netw, II 647-650, Beijing, 1992.

18) A recursive formula and its application to computations of normal forms and focal values, in Dynamical Systems, eds., S-T. Liao, et al.,238-247, World Sci.Publ., Singapore, 1993.

19) On periodic attractors of continuous Hopfield neural network consisting of two neurons(with W.Jin), Proc.China First Postdoctor Symp. (1993), ed. Feng Enbo, 1232-1235.

20) A simple proof and the improvement of the formula of computing Liapunov values given by Kertesz and Kooij(with L.Chen), J.Nanjing Univ., Math. quarterly,1993, 66-69.

21) Improved K-K algorithm for computing Lyapunov values, T.M.Math.Publ., Slovakia, 235-242.

22) A complex algorithm for Computing Liapunov values, (with Rei Mao), Random and computational dynamics, 2(2&3)(1994), 261-277.

23) Normal forms of a class of linear generalized Hamiltonian systems accociated semisimple Lie algebra, (with Jingping Wang), in Proc. of Tokyo conference on Dyamical systems, 1994.

24) Anouncement: Jumping property of Liapunov values , (with Rei Mao), Advances in Mathematics, 25:1(1996), 93-94.

25) Jumping property of Liapunov values, (with Rei Mao), Science in China, 39:12(1996), 1280-1287.

26) 一类人工神经网络的混沌, ‘96CSIAM 论文集, 198-202, 1996.

27) Linear grading function and further reduction of normal forms(with H.Kokubu and H.Oka), J.D.E.132:2(1996),293-318

28) Period Doubling-chaos-inverse Period Doubling Bifurcation in a Rotor-casing Dynamical System(with Wu Xianfang and Zhang Xiaozhang), Tsinghua Science and Technology, 2:3(1997),703-706

29) Isomorphism between systems of equivariant singularity, (with Xiaofeng Wang and Yun Tang), J.M.A.A.225(1998),26-45

30) Recognition and classification for O(n)-equivariant

bifurcation with O(n)-codimension less than 5, (with

Xiaofeng Wang and Yun Tang), Chin.Math.Ann. 19B:4(1998),

391-400

31) The closing lemma for non-singular endomorphisms

euivariant under free actions of finite groups, (with

Xiaofeng Wang), Transaction of Ame.Math.Soc. 351:10(1999),

4173-4182.

32)The unique normal form theory, Proc.Inter.Conf.Diff.Equa.

and comput.Simul. eds.W.Bates et al. World Scinific(1999),

316-321.

33) Unique normal form of Bogdanov-Takens singularities(with Li Jing, Huang Minhai, Jiang Yong), J.D.E., 163(2000),223-238.

34)Unique normal forms for the Takens-Bogdanov singularity in

a special case(with G.Chen and X.Wang), C.R.Acad.Sci.Paris,

t.332(2001), series I, 1-5.

35)General forms of the simplest normal forms of

Bogdanov_Takens singularities(with J.Li and W.Zhang),

Dynamics of continuous,discrete and impulsive systems,

Series A, Vol.8(2001), 519-530.

36) 一类具有正负系数的中立型方程的振动性（与张晓声合作），北京大学学报（自然科学版），185期（2002），11-17.

37)一类资产定价模型的动力学性质（与张晓声合作），第九届全球金

融年会论文选编，北京大学光华管理学院编，北京大学出版社，

2002，1032-1038．

38)A robust rational route to randomness in a simple asset

pricing model(with C.Hommes and H.Huang), preprint –02-08,

Center for Nonlinear Dynamics in Economics and Finance,

Faculty of Economics and Econometrics, University of

Amsterdam, the Netherlands, 2002.