共查询到20条相似文献,搜索用时 15 毫秒
1.
In the present paper, a class F of critically finite transcendental meromorphic functions having rational Schwarzian derivative is introduced and the dynamics of functions in one parameter family is investigated. It is found that there exist two parameter values λ∗=?(0)>0 and , where and is the real root of ?′(x)=0, such that the Fatou sets of fλ(z) for λ=λ∗ and λ=λ∗∗ contain parabolic domains. A computationally useful characterization of the Julia set of the function fλ(z) as the complement of the basin of attraction of an attracting real fixed point of fλ(z) is established and applied for the generation of the images of the Julia sets of fλ(z). Further, it is observed that the Julia set of fλ∈K explodes to whole complex plane for λ>λ∗∗. Finally, our results found in the present paper are compared with the recent results on dynamics of one parameter families λtanz, [R.L. Devaney, L. Keen, Dynamics of meromorphic maps: Maps with polynomial Schwarzian derivative, Ann. Sci. École Norm. Sup. 22 (4) (1989) 55-79; L. Keen, J. Kotus, Dynamics of the family λtan(z), Conform. Geom. Dynam. 1 (1997) 28-57; G.M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions, J. London Math. Soc. 49 (1994) 281-295] and , λ>0 [G.P. Kapoor, M. Guru Prem Prasad, Dynamics of : The Julia set and bifurcation, Ergodic Theory Dynam. Systems 18 (1998) 1363-1383]. 相似文献
2.
P. Domínguez A. Hernández G. Sienra 《Journal of Difference Equations and Applications》2013,19(7):1019-1032
We consider two classes of functions studied by Epstein [A.L. Epstein, Towers of finite type complex analytic maps, Ph.D. thesis, City University of New York, 1993] and by Herring [M.E. Herring, An extension of the Julia–Fatou theory of iteration, Ph.D. thesis, Imperial College, London, 1994], which have the Ahlfors' Property. We prove under some conditions on the Fatou and Julia sets that the singleton buried components are dense in the Julia set for these classes of functions. 相似文献
3.
ZHENG JianHua 《中国科学 数学(英文版)》2010,(3)
In this paper we make a further discussion of a relationship between the number of fixed-points and distribution of singular values along the round annuli centered at the origin of a transcendental meromorphic function. To attain our purpose we first establish a fundamental inequality for the modulus of derivative of a holomorphic covering mapping whose image is an annulus by virtue of the hyperbolic metric. The inequality is of independent significance. We make a simple survey on some domain constants for ... 相似文献
4.
Volker Mayer 《Mathematische Nachrichten》2009,282(8):1189-1194
We give a lower bound of the hyperbolic and the Hausdorff dimension of the Julia set of meromorphic functions of finite order under very general conditions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Ha Huy Khoai 《中国科学A辑(英文版)》2005,48(Z1)
In this paper we relate the study of unique range sets for meromorphic functions (URSM) with the hyperbolic hypersurfaces and give some remarks on the genericity of unique range sets for meromorphic functions. 相似文献
7.
We study Misiurewicz points on the parameter space about a family of rational maps Tλ concerning renormalization transformation in statistical mechanic. We determine the intersection points of the Julia set J(Tλ) and the positive real axis R+and discuss the continuity of the Hausdorff dimension HD(J(f)) about real parameter λ. 相似文献
8.
讨论了亚纯函数分担两个集合的唯一性问题,证明了一个定理.所得结果改进了先前的一些定理,例子表明结果是精确的. 相似文献
9.
JianMing Chang 《中国科学 数学(英文版)》2012,55(8):1669-1676
In this paper,we continue to study the normality of a family of meromorphic functions without simple zeros and simple poles such that their derivatives omit a given holomorphic function.Such a family in general is not normal at the zeros of the omitted function.Our main result is the characterization of the non-normal sequences,and hence some known results are its corollaries. 相似文献
10.
Given a sequence {fn } of meromorphic functions on a plane domain D, there exists a (possibly empty) open set U■D and a subsequence {f n k } which converges uniformly (with respect to the spherical metric on ) on compact subsets of U, while no subsequence of {f n k } converges uniformly on compact subsets of any larger open subset of D. 相似文献
11.
Cunji Yang 《分析论及其应用》2009,25(4):317-324
Based on the work of McMullen about the continuity of Julia set for rational functions, in this paper, we discuss the continuity
of Julia set and its Hausdorff dimension for a family of entire functions which satisfy some conditions. 相似文献
12.
In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases. 相似文献
13.
李效敏 《纯粹数学与应用数学》2002,18(2):109-115
研究了具有三个CM公共小函数对,一个IM公共小函数对的亚纯函数的惟一性,改进了李平与杨重骏,Brosch等人的有关结果,用例子说明本文的结果是最佳的. 相似文献
14.
Keaitsuda Maneeruk 《Journal of Mathematical Analysis and Applications》2005,306(1):218-226
Let M denote the class of functions f meromorphic outside some compact totally disconnected set E=E(f) and the cluster set of f at any a∈E with respect to is equal to . It is known that class M is closed under composition. Let f and g be two functions in class M, we study relationship between dynamics of f○g and g○f. Denote by F(f) and J(f) the Fatou and Julia sets of f. Let U be a component of F(f○g) and V be a component of F(g○f) which contains g(U). We show that under certain conditions U is a wandering domain if and only if V is a wandering domain; if U is periodic, then so is V and moreover, V is of the same type according to the classification of periodic components as U unless U is a Siegel disk or Herman ring. 相似文献
15.
Let f be a transcendental meromorphic function and Δf(z) = f(z + 1) − f(z). A number of results are proved concerning the existences of zeros and fixed points of Δ f(z) and Δ f(z)/f(z) when f(z) is of order σ(f)=1. Examples show that some of the results are sharp. 相似文献
16.
In this paper, we deal with the relation between the characteristic function of two nonconstant meromorphic functions with three weighted sharing values, which improves a result given by H.X. Yi and Y.H. Li. From this we establish a theorem which improves a result given by P. Li and C.C. Yang. 相似文献
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18.
S. Aleksanian 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(6):319-328
The paper discusses the problem of approximation of functions continuous on a closed stripe S h = {z: |Imz| ≤h} and holomorphic in its interior. The results relate to the uniform and tangential approximation of such functions f by meromorphic functions g with minimal growth in terms of Nevanlinna characteristic T (r, g). The growth depends on the growth of f in S h and certain differential properties of f on ?S h . It is assumed that the possible poles of g are restricted to the imaginary axis. 相似文献
19.
In this paper, we mainly discuss the normality of two families of functions concerning shared values and proved: Let F and G be two families of functions meromorphic on a domain D■C,a1, a2, a3, a4 be four distinct finite complex numbers. If G is normal, and for every f ∈ F , there exists g ∈ G such that f(z) and g(z) share the values a1, a2, a3, a4, then F is normal on D. 相似文献
20.
Jian-Hua Zheng 《Journal of Mathematical Analysis and Applications》2006,313(1):24-37
Let be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f(z) and proved, among others, that if f(z) has a Baker wandering domain U, then for all sufficiently large n, fn(U) contains a round annulus whose module tends to infinity as n→∞ and so for some 0<d<1,