Zalcman引理在随机迭代函数族动力系统中的应用

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

Zalcman引理在随机迭代函数族动力系统中的应用黄小杰^1,2, 刘芝秀¹1 南昌工程学院理学院江西 330099;
2 复旦大学计算机科学技术学院上海 200433 An Application of Zalcman Lemma in Dynamical Systems of Random Iterated Function Families Xiao Jie HUANG^1,2, Zhi Xiu LIU¹1 Department of Science, Nanchang Institute of Technology, Jiangxi 330099, P. R. China;
2 School of Computer Science and Technology, Fudan University, Shanghai 200433, P. R. China

摘要
图/表
参考文献
相关文章

全文: PDF(482 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要本文根据Schwick的思想，利用Zalcman引理讨论了随机迭代函数族动力系统，指出了函数族随机迭代动力系统的Fatou集和函数族衍生半群动力系统的Fatou集定义差别明显但却等价.并获得了如下正规定则，设F={f_i|f_i为C（C）上的非线性解析函数，i ∈ M}，其中M为非空指标集，Σ_M={（j₁，j₂，…，j_n，…）|j_i ∈ M，i ∈ N}，若对任意的指标序列σ=（j₁，j₂，…，j_n，…）∈ Σ_M，迭代序列{W_σⁿ=f_{j_n} º f_{j_n-1} º … ºf_j₁（z）|n ∈ N}在点z处正规，则函数族F本身在点z处正规.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2018-12-20

MR (2010):

O174.5

基金资助:国家自然科学基金资助项目（11671091，11731003）；江西省教育厅科技项目（GJJ180944，GJJ190963）

作者简介: 黄小杰,E-mail:xjhuang14@fudan.edu.cn;刘芝秀,E-mail:270144355@qq.com

引用本文:

黄小杰, 刘芝秀. Zalcman引理在随机迭代函数族动力系统中的应用[J]. 数学学报, 2020, 63(5): 531-536. Xiao Jie HUANG, Zhi Xiu LIU. An Application of Zalcman Lemma in Dynamical Systems of Random Iterated Function Families. Acta Mathematica Sinica, Chinese Series, 2020, 63(5): 531-536.

链接本文:

http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2020/V63/I5/531

[1] Baker I. N., Repulsive fixedpoints of entire functions, Math. Zeit., 1968, 104:252-256.
[2] Bargmann D., Simple proofs of some fundamental properties of the Julia set, Ergod. Th.& Dynam. Sys., 1999, 19:553-558.
[3] Bergweiler W., Iteration of meromorphic functions, Bulletin of the American Mathematical Society, 1993, 29(2):151-189.
[4] Fatou P., Sur les é quations fonctionnelles (in French), Bull. Soc. Math. France, 1920, 48:208-314.
[5] Gong Z. M., Ren F. Y., A random dynamical system formed by infinitely many functions, J. Fudan University, 1996, 35:387-392.
[6] Gu Y. X., Pang X. C., Fang M. L., The Theory of Normal Family and Its Application (in Chinese), Science Press, Beijing, 2007.
[7] Hinkkanen A., Martin G. J., The dynamics of semigroups of rational functions I, Proc. London Math. Soc., 1996, 73(3):358-384.
[8] Hinkkanen A., Martin G. J., Julia Sets of Rational Semigroups, Math. Z., 1996, 222(2):161-169.
[9] Jaerisch J., Sumi H., Dynamics of infinitely generated nicely expanding rational semigroups and the inducing method, Transactions of the American Mathematical Society, 2017, 369(9):6147-6187.
[10] Julia G., Memoire sur l'tération des fonctions rationnelles (in French), J. Math. Pure Appl., 1918, 8:47-245.
[11] Kriete H., Sumi H., Semihyperbolic transcendental semigroups, Journal of Mathematics of Kyoto University, 2000, 40(2):205-216.
[12] Ren F. Y., Qiu W. Y., Yin Y. C., et al., Complex Analytic Dynamical System (in Chinese), Fudan University Press, Shanghai, 1997.
[13] Schwick W., Repelling periodic points in the Julia set, Bulletin of the London Mathematical Society, 1997, 29(3):314-316.
[14] Stankewitz R., Density of repelling fixed points in the Julia set of a rational or entire semigroup, Journal of Difference Equations and Applications, 2010, 16(5-6):763-771.
[15] Stankewitz R., Density of repelling fixed points in the Julia set of a rational or entire semigroup II, Discrete and Continuous Dynamical Systems A, 2012, 32(7):2583-2589.
[16] Sumi H., Random complex dynamics and semigroups of holomorphic maps, Proceedings of the London Mathematical Society, 2011, 102(1):50-112.
[17] Yang L., Value Distribution Theory, Springer-Verlag & Science Press, Berlin, 1993.
[18] Zalcman L., A heuristic principle in complex function theory, American Mathematical Monthly, 1975, 82(8):813-817.
[19] Zhou W. M., Ren F. Y., Julia set of stochastic iterative system of transcendental entire functions (in Chinese), Chinese Science Bulletin, 1993, 38(4):289-289.

[1]	杨刘, 庞学诚. 多复变Pang-Zalcman引理及应用[J]. 数学学报, 2020, 63(6): 577-586.
[2]	文慧霞, 舒级, 李林芳. 一类非自治分数阶随机波动方程的随机吸引子[J]. 数学学报, 2019, 62(1): 25-40.
[3]	曾翠萍, 邓炳茂, 方明亮. 分担函数集的正规定则[J]. 数学学报, 2018, 61(4): 569-576.
[4]	仇惠玲, 方彩云, 方明亮. 涉及例外函数与分担函数的正规族[J]. Acta Mathematica Sinica, English Series, 2015, 58(2): 345-352.
[5]	刘晓毅, 程春暖. 正规族与分担函数[J]. Acta Mathematica Sinica, English Series, 2013, 56(6): 941-950.
[6]	王品玲, 刘丹, 方明亮. 分担值与具有重零点的亚纯函数正规族[J]. Acta Mathematica Sinica, English Series, 2013, 56(3): 343-352.
[7]	赵文强, 李扬荣. 带加法白噪声的随机Boussinesq方程组的解的渐近行为[J]. Acta Mathematica Sinica, English Series, 2013, 56(1): 1-14.
[8]	刘晓毅, 常建明. 分担集合的亚纯函数正规族[J]. Acta Mathematica Sinica, English Series, 2011, 54(6): 1049-1056.
[9]	徐焱, 常建明. 正规定则与重值[J]. Acta Mathematica Sinica, English Series, 2011, 54(2): 265-270.
[10]	张莎莎, 涂振汉. 多复变全纯函数族正规准则[J]. Acta Mathematica Sinica, English Series, 2010, 53(6): 1045-1050.
[11]	吕锋, 徐俊峰, 仪洪勋. 全纯函数的正规族[J]. Acta Mathematica Sinica, English Series, 2010, 53(5): 963-974.
[12]	陈俊凡. 与例外函数和分担函数相关的亚纯函数的正规族[J]. Acta Mathematica Sinica, English Series, 2010, 53(4): 655-662.
[13]	肖映青, 邱维元. Julia集和等势线上的Chebyshev多项式[J]. Acta Mathematica Sinica, English Series, 2010, 53(2): 323-328.
[14]	杨存基. 超整函数族Julia集的Hausdorff维数[J]. Acta Mathematica Sinica, English Series, 2010, 53(1): 187-198.
[15]	张庆德;秦春艳;. 亚纯函数的正规族与分担值[J]. Acta Mathematica Sinica, English Series, 2008, 51(1): 145-152.

PDF全文下载地址:

http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23638