郑建华   Jian-Hua Zheng 

Professor

Department of Mathematical Sciences, Tsinghua University
100084, Beijing, P. R. China
OFFICE: Room 1312, New Science Building, Tsinghua University
PHONE:  8610-62787953
EMAIL:  jzheng@math.tsinghua.edu.cn


Adavanced Mathematics (2)Fall, 2005


CV of Zheng Jian-Hua

 

Educations:        

Ph. D, Institute of Mathematics, Academia Sinica, 1992

                    Master Degree, Department of Mathematics, Anhui Normal University, 1987   

                  

Working Experience: Tsinghua University, Lecturer (1992-1993), Vice Professor(1993-1997), Professor(1997-present)

                    Anhui University, Lecturer (1990-1992)

 

Visiting Scholar:   Department of Mathematics, University of Norttingham, UK, 1995-1996.

                   

 

Awards:             学术新人奖,基础研究奖, 优秀教材一等奖(排名2)(Awards of Tsinghua University

                    北京市优秀教材一等奖(排名2

 

Researches:

 

Work on Complex Dynamics and Theory of Meromorphic Functions (including value distribution, factorization, differential equation in complex field).

The Fatou set and Julia set are main studying objects in complex dynamics. My main works in complex dynamics are on the uniform perfectness of the Julia set of a meromorphic function, relations between singularities and Fatou components (especially wandering domain and Baker domain) , non-existence of unbounded Fatou components, Lebsegue measure and Hausdorff dimension and invariant measure of the Julia set.

And my main works in theory of meromorphic functions are on permutability of entire functions, quantitative estimates of number of fixed points and factorization of composition of meromorphic functions and to establish an elementary method to discuss the growth of a meromorphic function with radially distributed values and to introduce a new singular direction, namely T direction and determine the existence of T direction and make a discussion of relation between T directions and the Nevanlinna deficient values.

 

Books: 《微积分(II)》高等教育出版社,2003 (普通高等教育“十五”国家级规划教材)( Calculus (II)

《复变函数》清华大学出版社,2005  (普通高等教育“十五”国家级规划教材)  ( Functions of one complex variable )

《亚纯函数动力学》(20045月完成,434页),清华大学学术专著,清华大学出版社,20066  ( Dynamics of a meromorphic function434 pages )

(该书出版后发现文献存在一些失误,由于编辑误用了没有修正的原文献目录排版,现附正确的文献,为此深表歉意!)

        Value Distribution of Meromorphic Functions Tsinghua University Press and Springer (联合出版),20106

 

学术交流:

 

120028月由日本资助参加在日本京都召开的国际数学家大会的卫星会议《New Directions in Dynamical Systems》,参加会议者共计约200人,包括许多顶尖的复动力系统专家,本人作25分钟报告《Iteration of functions meromorphic outside a small set》,听众约60多人。

220048月参加在泰国清迈大学召开的有限维与无限维分析会议,作邀请报告《亚纯函数的角域分布》,得到会议组资助。随后,访问数学系一个月,作《亚纯函数理论》的系列演讲。

320058月 组织参加了在新疆师范大学召开的会议,作大会报告《亚纯函数角分布综述》。

420031月 访问香港大学数学系讲:奇异值与稳定域间的关系。在香港科技大学讲:亚纯函数的角分布。

520034月 在肇庆学院演讲:数学的教育与学习。

620039月 访问汕头大学数学系,作《复动力系统》的系列演讲。

720041月起受香港裘槎基金资助作为裘槎访问学者访问香港大学数学系。讲:双曲度量与集合的一致完全性。

820044月 在深圳大学师范学院讲学:期望、信息和熵的理论基础,数学的教育与学习。中山大学讲:亚纯函数的遍历论。广州大学讲:亚纯函数的不变测度的存在性。

920045月 访问南京大学数学系讲:亚纯函数的遍历。

1020051月 在泰国基金会资助访问泰国清迈大学数学系。系列演讲:亚纯函数动力学中的问题。

1120055月 在江西师范大学讲学共两讲:亚纯函数理论。

1220064月 在华南师范大学讲:一个新的奇异方向;华南农业大学讲:具有射线分布值的亚纯函数特征;广州大学讲:奇异方向与亏值及其复域上的微分方程。

1320066月 北京航空航天大学讲:亚纯函数的特征与奇异方向。

1420067月 访问香港大学数学系约1个月。

1520068月 访问泰国清迈大学数学系,参加博士生答辩,作三次学术报告:1 整函数的可交换性;2 亚纯函数的特征;3 亚纯函数的幅角分布。

1620068月 访问长沙湖南师范大学数学学院,作学术报告:Walters膨胀理论在亚纯函数的不变测度研究中的应用。

17200611月 访问合肥中国科技大学数学系,作学术报告:亚纯函数的Baker域和游荡域。

18200612月 受邀在北京理工大学研究生论坛作报告:复动力系统简介

1920074  浙江大学宁波理工学院:双曲亚纯函数

2020078  山东威海国际复分析会议:亚纯函数奇异方向---T 方向

2120078~9  江西师范大学数学与信息学院组织举办研究生暑期班,系统讲解亚纯函数值分布理论

2220086  访问德国Kiel大学一周,作报告:Non-Existence of Unbounded Fatou Components of a Transcendental Meromorphic Function, 参加在Bremen召开的国际会议“Aspects of Transcendental Dynamics, 作报告:Dynamics of Hyperbolic Meromorphic Functions.

2320087  访问香港大学一个月

2420089  访问湖北咸宁学院,作报告:数学的教育与数学的美

25200810  参加复旦大学举办的Workshop, 作报告:Dimension, Poincare Exponent and Invariant Measure for Some Expanding Mappings; 访问上海交通大学,作报告:同上

26200911  参加南京大学的小型复动力系统会议,作报告:双曲度量与复动力系统

2720107  访问湖南长沙湖南师范大学,作报告:双曲度量与区域常数;长沙理工大学,作报告:值分布中的问题

2820107  访问华南师范大学, 作报告:值分布论中的位势理论

2920109  访问福州师范大学, 作报告:值分布中的问题

30201011月 参加在波兰科学院Banach 中心举办的超越函数动力系统会议,并作一小时报告,题为:Problems on dynamics of transcendental meromorphic functions.

3120116~7月 访问美国Illinoi大学香槟分校

3220118  参加南京大学数学系举办的复动力系统及复分析会议,并作报告:Thermodynamic formalism of meromorphic functions.

3320122 访问香港大学数学系,并作报告:Thermodynamic formalism of meromorphic functions.of finite type; 香港中文大学数学系,报告:Transfer operator of a continuous mapping with covering property.

 

 

 

 

Papers and Recent preprints (available in ps and pdf format)

 

53 Some examples of Baker domains, Nonlinearity, 25(2012), 1033-1044 (With Walter Bergweiler)

52 T and Hayman T points of meromorphic functions for small functions in the open unit disk, Acta Mathematica Scientia, 32B(4), (2012), 1662-1674 (With Wu Nan)

51 On the uniform perfectness of the boundary of multiply connected wandering domains, J. Austr. Math. Soc.. , 91(2011), 289-311 (With Walter Bergweiler)

50 Parabolic meromorphic functions, Pacific Math. J., vol.250, no.2 (2011), 487-509

49 On value distribution of meromorphic functions with respect to arguments I, Complex variables and elliptic equations: An international journal, vol.56, nos.1-4(2011), 271-298

48 Omitted values and dynamics of meromorphic functions, J. London Math. Soc.., (2)83(2011), 121-136 (With Tarakanta Nayak)

47 Hayman T directions of meromorphic functions, Taiwanese J. Math., vol.14, no.6 (2010), 2219-2228 (With Wu Nan)

46 On fixed-points and singular values of transcendental meromorphic functions, Science China Mathematics, vol.53,no.3(2010), 887-894.

45 Permutable entire functions satisfying linear differential equations J. Math. Anal. Appl.,354 (2009), 177-183 (With Piyapong Niasump and K. Maneeruk)

44 Non-existence of unbounded Fatou components of meromorphic functions, J. Math. Kyoto Univ., vol.49, no. 1(2009), 1-12 (With Piyapong Niasump)

43  Residual Julia sets of meromorphic functions, Math. Proc. Cambridge Phil. Soc.1412006),113-126.With Ng T. W. and Choi Y. Y.

42  On multiply-connected Fatou components in iteration of entire functions. J. Math. Anal . Appl.313(2006), 24-37.

41  Iteration of functions meromorphic outside a small set. Tohoku Math. J., 57(2005), 23-43

40  Boundedness of components of the Fatou set of entire and meromorphic functions. Indian J. Pure Appl. Math.,3510(2004), 1137-1148.(with S. Wang)

39  On transcendental meromorphic functions with radially distributed values. Science in China, Ser. A., Math., 33(6), (2003), 537-550 (in Chinese); 47(3),(2004), 401-416 (in English)

38  On a new singular direction of meromorphic functions. Bull. Austr. Math. Soc., 69(2004), 277-287. With Guo H. and Ng T. W.

37  On uniqueness of meromorphic functions with shared values in some angular domains.  Canadian J. Math.,47(1), 2004,152-160

36  Singularities and limit functions in iteration of meromorphic functions. J. London Math. Soc. ., (2)67(2003), 195-207

35  On uniqueness of meromorphic functions with four shared values in one angular domain. Complex Variables Th. and Appl. (An International Journal), 48 (9) (2003),777-786.

34  Some properties of Fatou and Julia sets of transcendental meromorphic functions. Bull. Austral. Math. Soc., vol. 66, (2002), 1-8 (With S. Wang and Z. G. Huang)

33  On uniformly perfect boundary of stable domains in iteration of meromorphic functions II, Math. Proc. Cambridge Phil. Soc.2002. vol. 132 (2002), 531-544.

32  On transcendental meromorphic functions which are geometrically finite, J. Austral. Math. Soc., vol. 72, no. 1 (2002), 93-107

31  On non-existence of unbounded domains of normality of meromorphic functionsJ. Math. Anal . Appl. vol. 264 (2001), 479-494

30  Uniformly perfect sets and distortion of holomorphic functions, Nagoya Math. J., vol. 1642001),17-33

29  On factorization of solutions of the second order linear differential equations, J. Math. Soc. Japan, vol. 53no.42001),835-845. With He YuZan

28  关于复合函数的值分布, 数学物理学报, 21A(2) 2001),167-170.

27  Singularities and wandering domains in iteration of meromorphic functions,  Illinois J. Math.vol. 44, no. 3, Fall 2000, 520-530.

26  Remarks on Herman rings of transcendental meromorphic functions, Indian J. Pure Appl. Math., 31(7), 2000, 747-751.

25  Unbounded domains of normality of entire functions of small growth,  Math. Proc. Cambridge Phil. Soc.,(128)(2000),355-361.

24  On uniformly perfect boundary of stable domains in iteration of meromorphic functions,  Bull. London Math. Soc., 32)(2000),439-446.

23  On the value distribution of iterated entire functions, J. Austral. Math. Soc., (Series A) 66 (1999), 18-31.

22  On the fixpoints, Multipliers and value distribution of certain classes of meromorphic functions, Ann. Acad. Sci. Fennicea Math. 23 (1998), 133-150. (With J. K. Langely)

21  On the growth of meromorphic functions with two radially distributed values, J. Math. Anal. Appl., 206 (1997), 140-154.

20  On the polynomial-value points of composite entire functions, Complex Variables, 34 (1997), 393-398. With C. C. Yang

19  Linear differential equations with rational coefficients, J. Math. Soc. Japan, 48 (3) (1996), 501-510.

18  On the fix-points of composite meromorphic functions and generalizations, J. Danal. Math. 68 (1996), 59-93 (With C. C. Yang)

    17  Further results on fixpoints and zeros of entire functions, Trans. Amer. Math. Soc., 347 (1) (1995), 37-50. (With C. C. Yang)

16  A remark on distribution of zeros of solutions of linear differential equations, Proc. Amer. Math. Soc. 123 (1995), 847-854

15  A note on the Riccati differential equations, J. Math. Anal. Appl. 109 (1995), 285-293

14  A quantitative estimate on fixpoints of composite meromorphic functions, Canad. Math. Bull. 38 (1995), 490-495

13  Estimate on the number of fixpoints of composite entire functions, Complex Variables, 24 (1994), 301-309.(With C. C. Yang

12  Family of analytic mappings between ultrahyperbolic surfaces, Acta Math. Sinica, New Series , 9 (1993), 414-420

11  On primeness of , J. Math. Anal. Appl. 176 (1993), 1-10 (With F. Gross and C. C. Yang)

10  Unique theorem for periodic meromorphic functions with three common values, Kexue Tongbao  37 (1992), 12-15 (in Chinese)

9   On the permutability of entire functions, J. Math. Anal. Appl. 167 (1992), 152-159. (With C. C. Yang)

8   Factorization of algebroid functions, Chin. J. Cont. Math. 13 (1992), 333-340/Chin. Ann. of Math. 13A: 5 (1992), 573-579 (With C. C. Yang)

7   Permutability of entire functions, Kodai Math. J., 15 (1992), 230-235.(With C. C. Yang)

6   Nonexistence of admissible solution of the function equation =1, Northeastein Math. J., 6 (1990), 60-64.

5   A class of prime periodic entire functions, J. Engineering Math. , 6 (1989), 70-74.

    4  On the 2nd power of prime meromorphic functions, Chin. Ann. Of Math., 10B (1989), 441-447.

    3  On permutability of periodic entire functions, J. Math. Anal. Appl., 140 (1989), 262-269.

    2  Permutability of entire functions satisfying certain differential equations, Tohoku Math. J., 40 (1988), 323-330. (With Zhou Z. Z.)

    1  On the factorization of several classes of entire functions, Kodai Math. J., 10 (1987), 328-334.

 

其它论文

 

1   谈大学数学微积分部分的教材改革,中国大学数学,教材研究

2   超越椭圆曲面到有限修改曲面的解析映照之投影族,清华大学学报,第2期,199615-21。(与王安斌)

3   全纯函数与其复合函数的正规族,清华大学学报,第2期,199650-52。(与韩云瑞)

4   函数分解论之新研究进展,国立编译馆馆刊,第二十一卷,第二期,1992373-398。(与杨重俊)

5   关于唯一性可分解的整函数,安徽师范大学学报,第1期,19907-12

6   满足方程的整函数间的关系,新疆师范大学学报,第2期,199015-19。(与何建勋)

7   Meromorphic functions with two radially distributed values, J. Math. Research and Exposition, vol. 10, no.4, 1990, 527

8   代数体函数的复合增长性及因子分解,自然杂志, vol. 12, no. 1, 1989, 876.

9   一类整函数的分解,安徽大学学报,第2期,19881-5

10  亚纯函数涉及慢增长函数的唯一性定理,安徽师范大学学报,第2期,1987 9-14

11  一类亚纯函数的正规定则,安徽师范大学学报,第2期,198688-95

 

待发表的论文

1        The dynamics of semigroups of meromorphic functions.

2        On value distribution of meromorphic functions with respect to arguments (52 pages).

3        Dynamics of Hyperbolic meromorphic functions.

4        Conformal measures, Poincare exponents and dimensions for a class of maps having covering property

5        Conformal and invariant measures of parabolic meromorphic functions, to appear in Houston Journal of Mathematics

6         On second order linear differential equations with periodic coefficients

7         Thermodynamical formalism of parabolic meromorphic functions